On the noncommutative differential geometry of semi-graded Artin-Schelter regular algebras
| dc.contributor.advisor | Reyes Villamil, Milton Armando | |
| dc.contributor.author | Rubiano Suárez, Andrés Alejandro | |
| dc.contributor.cvlac | Rubiano Suárez, Andrés Alejandro [0000180012] | |
| dc.contributor.googlescholar | Rubiano Suárez, Andrés Alejandro [g4fvDBIAAAAJ&hl] | |
| dc.contributor.orcid | Rubiano Suárez, Andrés Alejandro [0009-0009-1633-8018] | |
| dc.contributor.researchgate | Rubiano Suárez, Andrés Alejandro [Andres-Rubiano-11] | |
| dc.contributor.researchgroup | ||
| dc.date.accessioned | 2025-09-03T14:12:27Z | |
| dc.date.available | 2025-09-03T14:12:27Z | |
| dc.date.issued | 2024 | |
| dc.description | ilustraciones, diagramas | spa |
| dc.description.abstract | In this thesis we investigate the noncommutative differential geometry of families of semi-graded rings or semi-graded Artin-Schelter regular algebras. With this end, we present some definitions and preliminaries on these algebraic structures and on the smooth geometry of noncommutative algebras. We also present some differences between Artin-Schelter regular algebras and semi-graded Artin-Schelter regular algebras. Next, we concentrate our research on the smooth geometry of bi-quadratic algebras on three generators having PBW basis, double extension regular algebras of type (14641), diffusion algebras and skew Poincaré-Birkhoff-Witt extensions. Finally, we establish some related ideas with the aim of extending the Serre duality theorem for noncommutative projective schemes on graded algebras to the setting of semi-graded algebras. (Texto tomado de la fuente) | eng |
| dc.description.abstract | En esta tesis investigamos la geometría diferencial no conmutativa de familias de anillos semi-graduados o álgebras regulares Artin-Schelter semi-graduadas. Para ello, presentamos algunas definiciones y preliminares sobre estas estructuras algebraicas y sobre la geometría suave de álgebras no conmutativas. También presentamos algunas diferencias entre las álgebras regulares de Artin-Schelter y las álgebras regulares Artin-Schelter semi-graduadas. A continuación, concentramos nuestra investigación en la geometría suave de álgebras bicuadráticas en tres generadores que tienen base PBW, extensiones dobles de álgebras regulares de tipo (14641), álgebras de difusión y extensiones de Poincaré-Birkhoff-Witt torcidas. Finalmente, establecemos algunas ideas relacionadas con el objetivo de extender el teorema de dualidad de Serre para esquemas proyectivos no conmutativos en álgebras graduadas al entorno de álgebras semi-graduadas. | spa |
| dc.description.degreelevel | Doctorado | |
| dc.description.degreename | Doctor en ciencias - matemáticas | |
| dc.format.extent | vii, 188 páginas | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.instname | Universidad Nacional de Colombia | spa |
| dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia | spa |
| dc.identifier.repourl | https://repositorio.unal.edu.co/ | spa |
| dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/88570 | |
| dc.language.iso | eng | |
| dc.language.iso | spa | |
| dc.publisher | Universidad Nacional de Colombia | |
| dc.publisher.branch | Universidad Nacional de Colombia - Sede Bogotá | |
| dc.publisher.faculty | Facultad de Ciencias | |
| dc.publisher.place | Bogotá, Colombia | |
| dc.publisher.program | Bogotá - Ciencias - Doctorado en Ciencias - Matemáticas | |
| dc.relation.references | Atiyah, M. F., & MacDonald, I. G. (1969). Introduction to commutative algebra. Addison-Wesley Publishing Company. | |
| dc.relation.references | Rinehart, G. S. (1963). Differential forms on general commutative algebras. Transactions of the American Mathematical Society, 108(2), 195–222. | |
| dc.relation.references | McConnell, J. C. (1974). Representations of solvable Lie algebras and the Gelfand-Kirillov conjecture. Proceedings of the London Mathematical Society, 3(3), 453–484. | |
| dc.relation.references | Kirkman, E., Musson, I. M., & Passman, D. S. (1999). Noetherian down-up algebras. Proceedings of the American Mathematical Society, 127(11), 3161–3167. | |
| dc.relation.references | Bhattacharjee, A. (2020). Reflexive-nilpotents-property skewed by ring endomorphisms. Arab Journal of Mathematics, 9(1), 63–72. | |
| dc.relation.references | Kheradmand, M., Khabazian, H., Kwak, T. K., & Lee, Y. (2017). Reflexive property restricted to nilpotents. Journal of Algebra and Its Applications, 16(3), 1750044. | |
| dc.relation.references | Kwak, T. K., Lee, Y., & Yun, S. J. (2014). Reflexive property skewed by ring endomorphisms. Korean Journal of Mathematics, 22(2), 217–234. | |
| dc.relation.references | Verevkin, A. B. (1992). On a noncommutative analogue of the category of coherent sheaves on a projective scheme. American Mathematical Society Translations, 151(2). | |
| dc.relation.references | Krebs, K., & Sandow, S. (1997). Matrix product eigenstates for one-dimensional stochastic models and quantum spin chains. Journal of Physics A: Mathematical and General, 30(9), 3165–3173. | |
| dc.relation.references | Hamidizadeh, M., Hashemi, E., & Reyes, A. (2020). A classification of ring elements in skew PBW extensions over compatible rings. International Electronic Journal of Algebra, 28, 75–97. | |
| dc.relation.references | Bergman, G. M. (1978). The diamond lemma for ring theory. Advances in Mathematics, 29(2), 178–218. https://doi.org/10.1016/0001-8708(78)90010-5 | |
| dc.relation.references | Gabriel, P. (1962). Des catégories abéliennes. Bulletin de la Société Mathématique de France, 90, 328–448. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2021). Radicals and Köthe’s conjecture for skew PBW extensions. Communications in Mathematics and Statistics, 9(2), 119–138. | |
| dc.relation.references | Birkenmeier, G. F., Kim, J. Y., & Park, J. K. (2001). Polynomial extensions of Baer and quasi-Baer rings. Journal of Pure and Applied Algebra, 159, 24–42. | |
| dc.relation.references | Hashemi, E., Moussavi, A., & Haj Seyyed Javadi, H. (2003). Polynomial Ore extensions of Baer and p.p.-rings. Bulletin of the Iranian Mathematical Society, 29(2), 65–86. | |
| dc.relation.references | Hashemi, E., & Moussavi, A. (2005). Polynomial extensions of quasi-Baer rings. Acta Mathematica Hungarica, 107(3), 207–224. | |
| dc.relation.references | Hong, C. Y., Kim, N. K., & Kwak, T. K. (2000). Ore extensions of Baer and p.p.-rings. Journal of Pure and Applied Algebra, 151(3), 215–226. | |
| dc.relation.references | Hong, C. Y., Kim, N. K., & Kwak, T. K. (2003). On skew Armendariz rings. Communications in Algebra, 31(1), 103–122. | |
| dc.relation.references | Huh, C., Lee, Y., & Smoktunowicz, A. (2002). Armendariz rings and semicommutative rings. Communications in Algebra, 30(2), 751–761. | |
| dc.relation.references | Veerapen, P. (2017). Graded Clifford algebras and graded skew Clifford algebras and their role in the classification of Artin-Schelter regular algebras. Advances in Applied Clifford Algebras, 27(3), 2855–2871. | |
| dc.relation.references | Vancliff, M., & Van Rompay, K. (2000). Four dimensional regular algebras with point scheme, a nonsingular quadric in $\mathbb{P}^3$. Communications in Algebra, 28(5), 2211–2242. | |
| dc.relation.references | Vancliff, M. (2015). The interplay of algebra and geometry in the setting of regular algebras. MSRI Publications, 67, 371–390. | |
| dc.relation.references | Smith, S. P. (1991). A class of algebras similar to the enveloping of sl(2). Communications in Algebra, 322(1), 285–314. | |
| dc.relation.references | Cassidy, T., & Vancliff, M. (2010). Generalizations of graded Clifford algebras and of complete intersections. Journal of the London Mathematical Society, 81(1), 91–112. | |
| dc.relation.references | Verevkin, A. B. (1992). Serre injective sheaves. Matematicheskie Zametki, 52(4), 35–41. | |
| dc.relation.references | Grothendieck, A., & Dieudonné, J. (1961). Éléments de géométrie algébrique II. Publications Mathématiques de l’IHÉS, 8. | |
| dc.relation.references | Ahluwalia, D. V. (2002). Interface of gravitational and quantum realms. Modern Physics Letters A, 17(15n17), 1135–1145. World Scientific. | |
| dc.relation.references | Ajitabh, K., Smith, S. P., & Zhang, J. J. (1998). Auslander-Gorenstein rings. Communications in Algebra, 26(7), 2159–2180. Taylor & Francis. | |
| dc.relation.references | Albuquerque, H., & Majid, S. (1999). Quasialgebra structure of the octonions. Journal of Algebra, 220(1), 188–224. Elsevier. | |
| dc.relation.references | Alev, J., & Chamarie, M. (1992). Dérivations et automorphismes de quelques algèbres quantiques. Communications in Algebra, 20(6), 1787–1802. Taylor & Francis. | |
| dc.relation.references | Amelino-Camelia, G., & Majid, S. (2000). Waves on noncommutative space-time and gamma-ray bursts. International Journal of Modern Physics A, 15(27), 4301–4323. World Scientific. | |
| dc.relation.references | Andruskiewitsch, N., Angiono, I., & Heckenberger, I. (2018). Liftings of Jordan and super Jordan planes. Proceedings of the Edinburgh Mathematical Society, 61(3), 661–672. | |
| dc.relation.references | Andruskiewitsch, N., Angiono, I., & Heckenberger, I. (2021). On finite GK-dimensional Nichols algebras over abelian groups. Memoirs of the American Mathematical Society, 271. | |
| dc.relation.references | Andruskiewitsch, N., Bagio, D., Della Flora, S., & Flores, D. (2017). Representations of the super Jordan plane. São Paulo Journal of Mathematical Sciences, 11(2), 312–325. | |
| dc.relation.references | Apel, J. (1988). Gröbnerbasen in nichtkommutativen Algebren und ihre Anwendung (Tesis doctoral). University of Leipzig, Leipzig, Germany. | |
| dc.relation.references | Artamonov, V. A. (2015). Derivations of skew PBW-extensions. Communications in Mathematics and Statistics, 3(4), 449–457. | |
| dc.relation.references | Artin, M. (1992). Geometry of quantum planes. En D. Haile & J. Osterburg (Eds.), Azumaya algebras, actions and modules (Vol. 124, pp. 1–15). American Mathematical Society. | |
| dc.relation.references | Artin, M., & Schelter, W. (1987). Graded algebras of global dimension 3. Advances in Mathematics, 66(2), 171–216. | |
| dc.relation.references | Birkenmeier, G. F., Park, J. K., & Rizvi, S. T. (2013). Extensions of rings and modules. Birkhäuser. | |
| dc.relation.references | Brown, K., & Goodearl, K. R. (2002). Lectures on algebraic quantum groups. Birkhäuser-Verlag. | |
| dc.relation.references | Bueso, J., Gómez-Torrecillas, J., & Verschoren, A. (2003). Algorithmic methods in non-commutative algebra: Applications to quantum groups. Springer. | |
| dc.relation.references | Connes, A. (1994). Noncommutative geometry. Academic Press. | |
| dc.relation.references | Jordan, D. (2001). The graded algebra generated by two Eulerian derivatives. Algebras and Representation Theory, 4(3), 249–275. | |
| dc.relation.references | Kaplansky, I. (1968). Rings of operators. Benjamin. | |
| dc.relation.references | Krempa, J. (1996). Some examples of reduced rings. Algebra Colloquium, 3(4), 289–300. | |
| dc.relation.references | Lee, T. K., & Wong, T. L. (2003). On Armendariz rings. Houston Journal of Mathematics, 29(3), 583–593. | |
| dc.relation.references | Manin, Y. I. (1991). Topics in noncommutative geometry: M. B. Porter lectures (2nd ed.). Princeton University Press. | |
| dc.relation.references | Manin, Y. I. (1997). Gauge field theory and complex geometry (2nd ed., Vol. 289). Springer. | |
| dc.relation.references | Matczuk, J. (2004). A characterization of σ-rigid rings. Communications in Algebra, 32(11), 4333–4336. | |
| dc.relation.references | McConnell, J. C., & Robson, J. C. (2001). Noncommutative Noetherian rings (Vol. 30). American Mathematical Society. https://doi.org/10.1090/gsm/030 | |
| dc.relation.references | McKay, J., & Wang, S. (1988). An elementary proof of the automorphism theorem for the polynomial ring in two variables. Journal of Pure and Applied Algebra, 52(1–2), 91–102. | |
| dc.relation.references | Nagata, M. (1972). On the automorphism group of 𝕜[x, y]. Kinokuniya. | |
| dc.relation.references | Nasr-Isfahani, A. R., & Moussavi, A. (2008). Ore extensions of skew Armendariz rings. Communications in Algebra, 36(2), 508–522. | |
| dc.relation.references | Noether, E., & Schmeidler, W. (1920). Moduln in nichtkommutativen Bereichen, insbesondere aus Differential- und Differenzenausdrücken. Mathematische Zeitschrift, 8, 1–35. | |
| dc.relation.references | Redman, I. T. (1996). The noncommutative algebraic geometry of some skew polynomial algebras (Tesis doctoral). University of Wisconsin–Milwaukee, USA. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2017). PBW bases for some 3-dimensional skew polynomial algebras. Far East Journal of Mathematical Sciences, 101(6), 1207–1228. | |
| dc.relation.references | Rubiano, A. A. (2020). A view toward the geometry of normalizing sequences in finitely semi-graded algebras (Tesis de maestría). Universidad Nacional de Colombia, Bogotá, D. C., Colombia. | |
| dc.relation.references | Serre, P. (1955). Faisceaux algébriques cohérents. Annals of Mathematics, 61(2), 197–278. | |
| dc.relation.references | Shestakov, I. P., & Umirbaev, U. U. (2003). The tame and the wild automorphisms of polynomial rings in three variables. Journal of the American Mathematical Society, 17(1), 197–227. | |
| dc.relation.references | Van den Essen, A. (2000). Polynomial automorphisms and the Jacobian conjecture (Vol. 190). Birkhäuser-Verlag. | |
| dc.relation.references | Van Oystaeyen, F. (2000). Algebraic geometry for associative algebras. CRC Press. | |
| dc.relation.references | Abdi, M., & Talebi, Y. (2024). On the diameter of the zero-divisor graph over skew PBW extensions. Journal of Algebra and Its Applications, 23(5), 2450089. | |
| dc.relation.references | Artamonov, V., Lezama, O., & Fajardo, W. (2016). Extended modules and Ore extensions. Communications in Mathematics and Statistics, 4(2), 189–202. | |
| dc.relation.references | Artin, M., Tate, J., & Van den Bergh, M. (1991). Modules over regular algebras of dimension 3. Inventiones Mathematicae, 106(2), 335–388. | |
| dc.relation.references | Artin, M., Tate, J., & Van den Bergh, M. (2007). Some algebras associated to automorphisms of elliptic curves. En P. Cartier, L. Illusie, N. M. Katz, G. Laumon, Y. I. Manin, & K. A. Ribet (Eds.), The Grothendieck Festschrift. Volume I. A Collection of Articles Written in Honor of the 60th Birthday of Alexander Grothendieck (pp. 33–85). Birkhäuser Boston. | |
| dc.relation.references | Bavula, V. V. (1992). Generalized Weyl algebras and their representations. St. Petersburg Mathematical Journal, 4(1), 75–97. | |
| dc.relation.references | Bavula, V. V. (1996). Global dimension of generalized Weyl algebras. Canadian Mathematical Society Conference Proceedings, 18, 81–107. | |
| dc.relation.references | Bavula, V. V. (2023). Description of bi-quadratic algebras on 3 generators with PBW basis. Journal of Algebra, 631, 695–730. | |
| dc.relation.references | Bavula, V. V., & Al Khabyah, A. (2023). Bi-quadratic algebras on 3 generators with PBW: Class II.1. arXiv preprint. https://arxiv.org/abs/2312.17182 | |
| dc.relation.references | Berger, R. (1992). The quantum Poincaré–Birkhoff–Witt theorem. Communications in Mathematical Physics, 143(2), 215–234. | |
| dc.relation.references | Fajardo, W. (2018). Extended modules over skew PBW extensions [Tesis doctoral, Universidad Nacional de Colombia, Bogotá]. | |
| dc.relation.references | Gallego, C. (2015). Matrix methods for projective modules over σ-PBW extensions [Tesis doctoral, Universidad Nacional de Colombia, Bogotá]. | |
| dc.relation.references | Gómez, J. Y., & Suárez, H. (2020). Double Ore extensions versus graded skew PBW extensions. Communications in Algebra, 48(1), 185–197. | |
| dc.relation.references | Goodearl, K. R. (1990). Classical localizability in solvable enveloping algebras and Poincaré–Birkhoff–Witt extensions. Journal of Algebra, 132(1), 243–262. | |
| dc.relation.references | Green, H. S. (1953). A generalized method of field quantization. Physical Review, 90(2), 270–273. | |
| dc.relation.references | Greenberg, O. W., & Messiah, A. M. L. (1965). Selection rules for parafields and the absence of paraparticles in nature. Physical Review, 138(5B), B1155–B1167. | |
| dc.relation.references | Hamidizadeh, M., Hashemi, E., & Reyes, A. (2020). A classification of ring elements in skew PBW extensions over compatible rings. International Electronic Journal of Algebra, 28(1), 75–97. | |
| dc.relation.references | Hashemi, E., Khalilnezhad, K., & Alhevaz, A. (2017). (Σ, Δ)-Compatible skew PBW extension ring. Kyungpook Mathematical Journal, 57(3), 401–417. | |
| dc.relation.references | Havlíček, M., Klimyk, A. U., & Pošta, S. (2000). Central elements of the algebras U′(𝔰𝔬ₘ) and U(𝔦𝔰𝔬ₘ). Czechoslovak Journal of Physics, 50(1), 79–84. | |
| dc.relation.references | Higuera, S., & Reyes, A. (2022). A survey on the fusible property for skew PBW extensions. Journal of Algebraic Systems, 10(1), 1–29. | |
| dc.relation.references | Higuera, S., & Reyes, A. (2023). On weak annihilators and nilpotent associated primes of skew PBW extensions. Communications in Algebra, 51(11), 4839–4861. | |
| dc.relation.references | Jannussis, A., Leodaris, A., & Mignani, R. (1995). Non-Hermitian realization of a Lie-deformed Heisenberg algebra. Physics Letters A, 197(3), 187–191. | |
| dc.relation.references | Kanakoglou, K., & Daskaloyannis, C. (2009). Bosonisation and parastatistics. En S. Silvestrov, E. Paal, V. Abramov, & A. Stolin (Eds.), Generalized Lie Theory in Mathematics, Physics and Beyond (pp. 207–218). Springer. | |
| dc.relation.references | Karacuha, S. (2015). Aspects of noncommutative differential geometry [Tesis doctoral, Universidade do Porto]. | |
| dc.relation.references | Karacuha, S., & Lomp, C. (2014). Integral calculus on quantum exterior algebras. International Journal of Geometric Methods in Modern Physics, 11(4), 1450026. | |
| dc.relation.references | Lam, T. Y., Leroy, A., & Matczuk, J. (1997). Primeness, semiprimeness and prime radical of Ore extensions. Communications in Algebra, 25(8), 2459–2506. | |
| dc.relation.references | Lezama, O., & Venegas, H. (2020). Gelfand–Kirillov dimension for rings. São Paulo Journal of Mathematical Sciences, 14(1), 207–222. | |
| dc.relation.references | Li, Q. (2022). Double Ore extensions of anti-angle type for Hopf algebras. AIMS Mathematics, 7(7), 12566–12586. | |
| dc.relation.references | Lou, Q., Oh, S.-Q., & Wang, S. (2020). Poisson double extensions. Science China Mathematics, 63(4), 701–720. | |
| dc.relation.references | Lü, J., Oh, S.-Q., Wang, X., & Yu, X. (2018). Enveloping algebras of double Poisson–Ore extensions. Communications in Algebra, 46(11), 4891–4904. | |
| dc.relation.references | Lü, J., Wang, X., & Zhuang, G. (2015). Universal enveloping algebras of Poisson Ore extensions. Proceedings of the American Mathematical Society, 143(11), 4633–4645. | |
| dc.relation.references | Marubayashi, H., & Zhang, Y. (1996). Maximality of PBW extensions of orders. Communications in Algebra, 24(4), 1377–1388. | |
| dc.relation.references | Matczuk, J. (1988). The Gelfand–Kirillov dimension of Poincaré–Birkhoff–Witt extensions. En F. Van Oystaeyen & L. Le Bruyn (Eds.), Perspectives in Ring Theory (pp. 221–226). Springer. | |
| dc.relation.references | McConnell, J. C., & Pettit, J. J. (1988). Crossed products and multiplicative analogues of Weyl algebras. Journal of the London Mathematical Society, 38(1), 47–55. | |
| dc.relation.references | Reyes, A. (2013). Ring and module theoretical properties of skew PBW extensions [Tesis doctoral, Universidad Nacional de Colombia, Bogotá]. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2020). Skew Poincaré–Birkhoff–Witt extensions over weak compatible rings. Journal of Algebra and Its Applications, 19(12), 2050225. | |
| dc.relation.references | Suárez, H. (2017). N-Koszul algebras, Calabi–Yau algebras and skew PBW extensions [Tesis doctoral, Universidad Nacional de Colombia, Bogotá]. | |
| dc.relation.references | Suárez, H., Higuera, S., & Reyes, A. (2024). On Σ-skew reflexive-nilpotents-property for rings. Algebra and Discrete Mathematics, 37(1), 134–159. | |
| dc.relation.references | Suárez, H., & Reyes, A. (2017). A generalized Koszul property for skew PBW extensions. Far East Journal of Mathematical Sciences, 101(2), 301–320. | |
| dc.relation.references | Van Oystaeyen, F., & Willaert, L. A. (1995). Grothendieck topology, coherent sheaves and Serre’s theorem for schematic algebras. Journal of Pure and Applied Algebra, 104(1), 109–122. | |
| dc.relation.references | Van Oystaeyen, F., & Willaert, L. A. (1996). Cohomology of schematic algebras. Journal of Algebra, 185(1), 74–84. | |
| dc.relation.references | Van Oystaeyen, F., & Willaert, L. A. (1996). The quantum site of a schematic algebra. Communications in Algebra, 24(1), 209–222. | |
| dc.relation.references | Van Oystaeyen, F., & Willaert, L. A. (1997). Examples and quantum sections of schematic algebras. Journal of Pure and Applied Algebra, 120(2), 195–211. | |
| dc.relation.references | Venegas, H. (2020). Zariski cancellation problem for skew PBW extensions [Tesis doctoral, Universidad Nacional de Colombia, Bogotá]. | |
| dc.relation.references | Zhedanov, A. S. (1991). “Hidden symmetry” of Askey–Wilson polynomials. Theoretical and Mathematical Physics, 89(2), 1146–1157. | |
| dc.relation.references | Akalan, E., & Marubayashi, H. (2016). Multiplicative ideal theory in noncommutative rings. En S. Chapman, M. Fontana, A. Geroldinger, & B. Olberding (Eds.), Multiplicative ideal theory and factorization theory. Commutative and non-commutative perspectives (pp. 1–22). Springer. | |
| dc.relation.references | Benkart, G. (1999). Down-up algebras and Witten’s deformation of the universal enveloping algebra of 𝔰𝔩₂. Contemporary Mathematics, 224, 29–46. American Mathematical Society. | |
| dc.relation.references | Beggs, E., & Majid, S. (2014). Gravity induced from quantum spacetime. Classical and Quantum Gravity, 31(3), 035020. | |
| dc.relation.references | Beggs, E. J., & Brzeziński, T. (2005). The Serre spectral sequence of a noncommutative fibration for de Rham cohomology. Acta Mathematica, 195(2), 155–196. | |
| dc.relation.references | Beggs, E. J., & Majid, S. (2020). Quantum Riemannian geometry (Vol. 355). Springer. | |
| dc.relation.references | Bellamy, G., Rogalski, D., Schedler, T., Stafford, J. T., & Wemyss, M. (2016). Noncommutative algebraic geometry (Vol. 64). Cambridge University Press. | |
| dc.relation.references | Berger, M. (2000). Riemannian geometry during the second half of the twentieth century (Vol. 17). American Mathematical Society. | |
| dc.relation.references | Brzeziński, T. (2011). Divergences on projective modules and noncommutative integrals. International Journal of Geometric Methods in Modern Physics, 8(4), 885–896. | |
| dc.relation.references | Brzeziński, T. (2014). On the smoothness of the noncommutative pillow and quantum teardrops. SIGMA. Symmetry, Integrability and Geometry: Methods and Applications, 10, 015, 1–8. | |
| dc.relation.references | Brzeziński, T. (2015). Differential smoothness of affine Hopf algebras of Gelfand–Kirillov dimension two. Colloquium Mathematicum, 139(111–119), 413–449. | |
| dc.relation.references | Brzeziński, T., & Lomp, C. (2018). Differential smoothness of skew polynomial rings. Journal of Pure and Applied Algebra, 222(9), 2413–2426. | |
| dc.relation.references | Brzeziński, T., & Sitarz, A. (2017). Smooth geometry of the noncommutative pillow, cones and lens spaces. Journal of Noncommutative Geometry, 11(2), 413–449. | |
| dc.relation.references | Brzeziński, T., Ciccoli, N., Dąbrowski, L., & Sitarz, A. (2016). Twisted reality condition for Dirac operators. Mathematical Physics, Analysis and Geometry, 19(3), 1–11. | |
| dc.relation.references | Brzeziński, T., Dąbrowski, H., & Rembieliński. (1992). On the quantum differential calculus and the quantum holomorphicity. Journal of Mathematical Physics, 33(1), 19–24. | |
| dc.relation.references | Brzeziński, T., El Kaoutit, L., & Lomp, C. (2010). Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry, 4(2), 281–312. | |
| dc.relation.references | Cassidy, T., & Vancliff, M. (2010). Generalizations of graded Clifford algebras and of complete intersections. Journal of the London Mathematical Society, 81(1), 91–112. | |
| dc.relation.references | Cassidy, T., & Vancliff, M. (2014). Corrigendum: Generalizations of graded Clifford algebras and of complete intersections. Journal of the London Mathematical Society, 90(2), 631–636. | |
| dc.relation.references | Chacón, A., & Reyes, A. (2024). On the schematicness of some Ore polynomials of higher order generated by homogenous quadratic relations. Journal of Algebra and Its Applications. Advance online publication. https://doi.org/10.1142/S021949882550207X | |
| dc.relation.references | Doplicher, S., Fredenhagen, K., & Roberts, J. (1995). The quantum structure of spacetime at the Planck scale and quantum fields. Communications in Mathematical Physics, 172(1), 187–220. | |
| dc.relation.references | Fajardo, W., Lezama, O., Payares, C., Reyes, A., & Rodríguez, C. (2024). Introduction to algebraic analysis on Ore extensions. En A. Martsinkovsky (Ed.), Functor categories, model theory, algebraic analysis and constructive methods (FCMT CCT2 2022, Almería, Spain, July 11–15). Invited and selected contributions (Vol. 450, pp. 45–116). Springer. | |
| dc.relation.references | Giesbrecht, M. W., Labahn, G., & Zhang, Y. (2014). Computing Popov forms of matrices over PBW extensions. En R. Feng, W. Lee, & Y. Sato (Eds.), Computer mathematics. 9th Asian Symposium (ASCM 2009), Fukuoka, December 2009; 10th Asian Symposium (ASCM 2012), Beijing, October 2012. Contributed papers and invited talks (pp. 61–65). Springer. | |
| dc.relation.references | Giesbrecht, M. W., Reid, G. J., & Zhang, Y. (2002). Non-commutative Gröbner bases in Poincaré–Birkhoff–Witt extensions. En V. G. Ganzha, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Proceedings of the Fifth International Workshop on Computer Algebra in Scientific Computing (CASC 2002), Yalta, Ukraine (pp. 97–106). Technical University of Munich. | |
| dc.relation.references | Gómez-Torrecillas, J. G. (2014). Basic module theory over non-commutative rings with computational aspects of operator algebras. En M. Barkatou, T. Cluzeau, G. Regensburger, & M. Rosenkranz (Eds.), Algebraic and algorithmic aspects of differential and integral operators (AADIOS 2012) (Vol. 8372, pp. 23–82). Springer. | |
| dc.relation.references | Hayashi, T. (1990). Q-analogues of Clifford and Weyl algebras: Spinor and oscillator representations of quantum enveloping algebras. Communications in Mathematical Physics, 127(1), 129–144. | |
| dc.relation.references | Jordan, D. A. (1995). Finite-dimensional simple modules over certain iterated skew polynomial rings. Journal of Pure and Applied Algebra, 98(1), 45–55. | |
| dc.relation.references | Krahmer, U. (2012). On the Hochschild (co)homology of quantum homogeneous spaces. Israel Journal of Mathematics, 189(1), 237–266. | |
| dc.relation.references | Louzari, M., & Reyes, A. (2020). Generalized rigid modules and their polynomial extensions. En M. Siles Molina, L. El Kaoutit, M. Louzari, L. Ben Yakoub, & M. Benslimane (Eds.), Associative and non-associative algebras and applications (MAMAA 2018) (Vol. 311, pp. 147–158). Springer. | |
| dc.relation.references | Montgomery, S. (1993). Hopf algebras and their actions on rings (Vol. 82). American Mathematical Society. https://doi.org/10.1090/cbms/082 | |
| dc.relation.references | Niño, A., Ramírez, M. C., & Reyes, A. (2020). Associated prime ideals over skew PBW extensions. Communications in Algebra, 48(12), 5038–5055. | |
| dc.relation.references | Niño, A., Ramírez, M. C., & Reyes, A. (2024). A first approach to the Burchnall–Chaundy theory for quadratic algebras having PBW bases. arXiv preprint. https://arxiv.org/abs/2401.10023 | |
| dc.relation.references | Reyes, A., & Suárez, H. (2016). A note on zip and reversible skew PBW extensions. Boletín de Matemáticas, 23(1), 71–79. | |
| dc.relation.references | Seiler, W. M. (2010). Involution: The formal theory of differential equations and its applications in computer algebra (Vol. 24). Springer. | |
| dc.relation.references | Suárez, H., Chacón, A., & Reyes, A. (2022). On NI and NJ skew PBW extensions. Communications in Algebra, 50(2), 3261–3275. | |
| dc.relation.references | Suárez, H., Reyes, A., & Suárez, Y. (2023). Homogenized skew PBW extensions. Arabian Journal of Mathematics, 12(1), 247–263. | |
| dc.relation.references | Tumwesigye, A. B., Richter, J., & Silvestrov, S. (2020). Centralizers in PBW extensions. En S. Silvestrov, A. Malyarenko, & M. Rančić (Eds.), Algebraic structures and applications (SPAS 2017) (Vol. 317, pp. 469–490). Springer. | |
| dc.relation.references | Willaert, L. (1997). Schematic algebras and the Auslander–Gorenstein property. En J. Alev & G. Cauchon (Eds.), Algèbre non commutative, groupes quantiques et invariants. Proceedings of the 7th Franco-Belgian Conference, Reims, June 26–30, 1995 (pp. 149–156). Société Mathématique de France. | |
| dc.relation.references | Yamane, H. (1989). A Poincaré–Birkhoff–Witt theorem for quantized universal enveloping algebras of type Aₙ. Publications of the Research Institute for Mathematical Sciences, Kyoto University, 25(3), 503–520. | |
| dc.relation.references | Zhang, J. J. (1996). Twisted graded algebras and equivalences of graded categories. Proceedings of the London Mathematical Society, 72(2), 281–311. | |
| dc.relation.references | Gallego, C., & Lezama, O. (2010). Gröbner bases for ideals of σ-PBW extensions. Communications in Algebra, 39(1), 50–75. Taylor & Francis. | |
| dc.relation.references | Gallot, S., Hulin, D., & Lafontaine, J. (1990). Riemannian geometry (Vol. 2). Springer. | |
| dc.relation.references | Giachetta, G., Mangiarotti, L., & Sardanashvili, G. (2005). Geometric and algebraic topological methods in quantum mechanics. World Scientific. | |
| dc.relation.references | Gudmundsson, S. (2004). An introduction to Riemannian geometry. Lecture Notes version, 1–235. | |
| dc.relation.references | Kiefer, C. (2006). Quantum gravity: General introduction and recent developments. Annalen der Physik, 15(1–2), 129–148. Wiley Online Library. | |
| dc.relation.references | Kirillov, A. (2008). An introduction to Lie groups and Lie algebras (Vol. 113). Cambridge University Press. | |
| dc.relation.references | Knapp, A. (2013). Lie groups beyond an introduction (Vol. 140). Springer. | |
| dc.relation.references | Krull, W. (1925). Über verallgemeinerte endliche Abelsche Gruppen. Mathematische Zeitschrift, 23(1), 161–196. Springer. | |
| dc.relation.references | Leinster, T. (2014). Basic category theory (Vol. 143). Cambridge University Press. | |
| dc.relation.references | Lezama, O., & Latorre, E. (2017). Non-commutative algebraic geometry of semi-graded rings. International Journal of Algebra and Computation, 27(4), 361–389. World Scientific. | |
| dc.relation.references | Lezama, O., Acosta, J. P., & Reyes, A. (2015). Prime ideals of skew PBW extensions. Revista de la Unión Matemática Argentina, 56(2), 39–55. | |
| dc.relation.references | Lezama, O., & Gómez, J. (2019). Koszulity and point modules of finitely semi-graded rings and algebras. Symmetry, 11(7), 881. MDPI. | |
| dc.relation.references | Lezama, O., & Reyes, A. (2014). Some homological properties of skew PBW extensions. Communications in Algebra, 42(3), 1200–1230. | |
| dc.relation.references | Chacón, A., & Reyes, A. (2024). Noncommutative scheme theory and the Serre–Artin–Zhang–Verevkin theorem for semi-graded rings. Journal of Noncommutative Geometry. Advance online publication. https://arxiv.org/abs/2301.07815 | |
| dc.relation.references | Higuera, S., Ramírez, M. C., & Reyes, A. (2024). On the uniform dimension and the associated primes of skew PBW extensions. Boletín de la Sociedad Matemática Brasileña (N.S.). Advance online publication. | |
| dc.relation.references | Higuera, S., & Reyes, A. (2024). Attached prime ideals over skew Ore polynomials. Communications in Algebra. Advance online publication. https://doi.org/10.1080/00927872.2024.2400578 | |
| dc.relation.references | Lezama, O., Wang, Y. H., & Zhang, J. J. (2019). Zariski cancellation problem for non-domain noncommutative algebras. Mathematische Zeitschrift, 292(3–4), 1269–1290. | |
| dc.relation.references | Chacón, A., Ramírez, M. C., & Reyes, A. (2024). Maps between schematic semi-graded rings. Beiträge zur Algebra und Geometrie. Advance online publication. https://arxiv.org/abs/2401.15631 | |
| dc.relation.references | Niño, A., & Reyes, A. (2024). On centralizers and pseudo-multidegree functions for non-commutative rings having PBW bases. Journal of Algebra and Its Applications. Advance online publication. https://doi.org/10.1142/S0219498825501099 | |
| dc.relation.references | Fajardo, W., Gallego, C., Lezama, O., Reyes, A., Suárez, H., & Venegas, H. (2020). Skew PBW extensions: Ring and module-theoretic properties, matrix and Gröbner methods, and applications. Springer. | |
| dc.relation.references | Mac Lane, S. (2013). Categories for the working mathematician (Vol. 5). Springer. | |
| dc.relation.references | Mackenzie, K., Kirill, M., & Mackenzie, K. C. (1987). Lie groupoids and Lie algebroids in differential geometry (Vol. 124). Cambridge University Press. | |
| dc.relation.references | Majid, S. (2019). Quantum Riemannian geometry and particle creation on the integer line. Classical and Quantum Gravity, 36(13), 135011. | |
| dc.relation.references | Bavula, V. V. (2020). Generalized Weyl algebras and diskew polynomial rings. Journal of Algebra and Its Applications, 19(10), 2050194. | |
| dc.relation.references | Majid, S. (2000). Quantum groups and noncommutative geometry. Journal of Mathematical Physics, 41(6), 3892–3942. | |
| dc.relation.references | McConnell, J., Robson, J., & Small, L. (2001). Noncommutative Noetherian rings (2nd ed., Vol. 30). American Mathematical Society. | |
| dc.relation.references | Mitchell, B. (1965). Theory of categories (Vol. 17). Academic Press. | |
| dc.relation.references | Nafari, M., & Vancliff, M. (2015). Graded skew Clifford algebras that are twists of graded Clifford algebras. Communications in Algebra, 43(2), 719–725. Taylor & Francis. | |
| dc.relation.references | Nathanson, M. B. (2018). An elementary proof for the Krull dimension of a polynomial ring. American Mathematical Monthly, 125(7), 623–637. Taylor & Francis. | |
| dc.relation.references | Polishchuk, A., & Positselski, L. (2005). Quadratic algebras (Vol. 37). American Mathematical Society. | |
| dc.relation.references | Reyes, A. (2014). Uniform dimension over skew PBW extensions. Revista Colombiana de Matemáticas, 48(1), 79–96. | |
| dc.relation.references | Reyes, A., & Sarmiento, C. (2022). On the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras. International Journal of Algebra and Computation, 32(3), 529–559. | |
| dc.relation.references | Rosenberg, A. (2013). Noncommutative algebraic geometry and representations of quantized algebras (Vol. 330). Springer. | |
| dc.relation.references | Rovelli, C. (2004). Quantum gravity. Cambridge University Press. | |
| dc.relation.references | Samelson, H. (2012). Notes on Lie algebras. Springer. | |
| dc.relation.references | Zhu, C., van Oystaeyen, F., & Zhang, Y. (2017). Nakayama automorphisms of double Ore extensions of Koszul regular algebras. Manuscripta Mathematica, 152(3–4), 555–584. | |
| dc.relation.references | Lezama, O., Reyes, A., & Suárez, H. (2017). Calabi–Yau property for graded skew PBW extensions. Revista Colombiana de Matemáticas, 51(2), 221–239. | |
| dc.relation.references | Suárez, H., Cáceres, D., & Reyes, A. (2021). Some special types of determinants in graded skew PBW extensions. Revista Integración, 39(1), 91–107. | |
| dc.relation.references | Cassidy, T., & Vancliff, M. (2010). Generalizations of graded Clifford algebras and of complete intersections. Journal of the London Mathematical Society, 81(1), 91–112. | |
| dc.relation.references | Phan, C. (2012). The Yoneda algebra of a graded Ore extension. Communications in Algebra, 40(3), 834–844. | |
| dc.relation.references | Cassidy, T., & Shelton, B. (2008). Generalizing the notion of Koszul algebra. Mathematische Zeitschrift, 260(1), 93–114. | |
| dc.relation.references | Suárez, H. (2017). Koszulity for graded skew PBW extensions. Communications in Algebra, 45(10), 4569–4580. | |
| dc.relation.references | Teunissen, P. J., & Kleusberg, A. (2012). GPS for geodesy. Springer. | |
| dc.relation.references | Vancliff, M. (2015). The interplay of algebra and geometry in the setting of regular algebras. En Commutative algebra and noncommutative algebraic geometry (Vol. 6, pp. 371–390). Cambridge University Press. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2017). σ-PBW extensions of skew Armendariz rings. Advances in Applied Clifford Algebras, 27(4), 3197–3224. | |
| dc.relation.references | Veerapen, P. (2017). Graded Clifford algebras and graded skew Clifford algebras and their role in the classification of Artin–Schelter regular algebras. Advances in Applied Clifford Algebras, 27(3), 2855–2871. | |
| dc.relation.references | Lezama, O. (2022). Cuadernos de álgebra, volumen 2: Anillos y módulos, categorías, álgebra homológica, álgebra no conmutativa, geometría algebraica. Facultad de Ciencias, Universidad Nacional de Colombia. | |
| dc.relation.references | Sweedler, M. E. (1969). Hopf algebras. W. A. Benjamin. | |
| dc.relation.references | Underwood, R. G. (2011). An introduction to Hopf algebras. Springer. | |
| dc.relation.references | Kurakin, V. L. (2002). Hopf algebra dual to a polynomial algebra over a commutative ring. Mathematical Notes, 71(5–6), 617–623. Springer. | |
| dc.relation.references | Hall, B. C. (2003). Lie groups, Lie algebras, and representations: An elementary introduction (Vol. 222). Springer. | |
| dc.relation.references | Humphreys, J. E. (1972). Introduction to Lie algebras and representation theory (Vol. 9). Springer. | |
| dc.relation.references | Helgason, S. (2001). Differential geometry and symmetric spaces (Vol. 341). American Mathematical Society. | |
| dc.relation.references | Jacobson, N. (1979). Lie algebras. Dover. | |
| dc.relation.references | Kharchenko, V. (2015). Quantum Lie theory: A multilinear approach (Vol. 2150). Springer. | |
| dc.relation.references | Montgomery, S. (2009). Hopf Galois theory: A survey. En A. Baker & B. Richter (Eds.), New topological contexts for Galois theory and algebraic geometry (BIRS 2008) (Vol. 16, pp. 367–400). Geometry and Topology Monographs. | |
| dc.relation.references | Schneider, H.-J. (1990). Representation theory of Hopf Galois extensions. Israel Journal of Mathematics, 72(1–2), 196–231. | |
| dc.relation.references | Kassel, C. (1995). Quantum groups (Vol. 155). Springer. | |
| dc.relation.references | Rotman, J. (2008). An introduction to homological algebra. Springer. | |
| dc.relation.references | Krause, G., & Lenagan, T. (2000). Growth of algebras and Gelfand–Kirillov dimension (Vol. 22). American Mathematical Society. | |
| dc.relation.references | Higgins, P. (1969). Baer invariants and the Birkhoff-Witt theorem. Journal of Algebra, 11(4), 469–482. Academic Press. | |
| dc.relation.references | Cohn, P. (1963). A remark on the Birkhoff-Witt theorem. Journal of the London Mathematical Society, s1-38(1), 197–203. https://doi.org/10.1112/jlms/s1-38.1.197 | |
| dc.relation.references | Kaplansky, I. (1970). Commutative rings. Allyn and Bacon. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2016). Some remarks about the cyclic homology of skew PBW extensions. Ciencia en Desarrollo, 7(2), 99–107. Universidad Pedagógica y Tecnológica de Colombia. | |
| dc.relation.references | Rogalski, D. (2024). Artin–Schelter regular algebras. En K. A. Brown, T. J. Hodges, M. Vancliff, & J. J. Zhang (Eds.), Recent advances in noncommutative algebra and geometry (Vol. 801, pp. 195–242). American Mathematical Society. | |
| dc.relation.references | Suárez, H., & Reyes, A. (2017). Koszulity for skew PBW extensions over fields. JP Journal of Algebra, Number Theory and Applications, 39(2), 181–203. | |
| dc.relation.references | Vancliff, M., & Van Rompay, K. (1997). Embedding a quantum nonsingular quadric in a quantum $\mathbb{P}^3$. Journal of Algebra, 195(1), 93–129. Elsevier. | |
| dc.relation.references | Shelton, B., & Vancliff, M. (2002). Schemes of line modules I. Journal of the London Mathematical Society, 65(3), 575–590. Cambridge University Press. | |
| dc.relation.references | Lezama, O. (2020). Computation of point modules of finitely semi-graded rings. Communications in Algebra, 48(2), 866–878. | |
| dc.relation.references | Goodearl, K. R., & Warfield, R. B., Jr. (2004). An introduction to noncommutative Noetherian rings (Vol. 61). Cambridge University Press. https://doi.org/10.1017/cbo9780511841699 | |
| dc.relation.references | Vancliff, M. (2015). On the notion of complete intersection outside the setting of skew polynomial rings. Communications in Algebra, 43(2), 460–470. Taylor & Francis. | |
| dc.relation.references | Hartshorne, R. (1977). Algebraic geometry. Springer. | |
| dc.relation.references | Greuel, G., & Pfister, G. (2012). A singular introduction to commutative algebra. Springer. | |
| dc.relation.references | Lezama, O., & Venegas, H. (2020). Gelfand–Kirillov dimension for rings. São Paulo Journal of Mathematical Sciences, 14(1), 207–222. | |
| dc.relation.references | Reyes, A. (2013). Gelfand–Kirillov dimension of skew PBW extensions. Revista Colombiana de Matemáticas, 47(1), 95–111. | |
| dc.relation.references | Golovashkin, A. V., & Maksimov, V. M. (1998). Skew Ore polynomials of higher orders generated by homogeneous quadratic relations. Russian Mathematical Surveys, 53(2), 384–386. | |
| dc.relation.references | Golovashkin, A. V., & Maksimov, V. M. (2005). On algebras of skew polynomials generated by quadratic homogeneous relations. Journal of Mathematical Sciences, 129(2), 3757–3771. | |
| dc.relation.references | Lezama, O. (2017). Some homological properties of skew PBW extensions arising in non-commutative algebraic geometry. Discussiones Mathematicae. General Algebra and Applications, 37(1), 45–57. | |
| dc.relation.references | Reyes, A. (2019). Armendariz modules over skew PBW extensions. Communications in Algebra, 47(3), 1248–1270. | |
| dc.relation.references | Gallego, C., & Lezama, O. (2017). Projective modules and Gröbner bases for skew PBW extensions. Dissertationes Mathematicae, 521, 1–50. | |
| dc.relation.references | Jiménez, H., & Lezama, O. (2015). Gröbner bases for modules over sigma-PBW extensions. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis (N.S.), 31(3). | |
| dc.relation.references | Reyes, A., & Suárez, H. (2017). Enveloping algebra and skew Calabi–Yau algebras over skew Poincaré–Birkhoff–Witt extensions. Far East Journal of Mathematical Sciences, 102(2), 373–397. | |
| dc.relation.references | Niño, A., & Reyes, A. (2017). Some ring theoretical properties of skew Poincaré–Birkhoff–Witt extensions. Boletín de Matemáticas, 24(2), 131–148. | |
| dc.relation.references | Reyes, A., & Suárez, H. (2017). Bases for quantum algebras and skew Poincaré–Birkhoff–Witt extensions. Momento, 1(54), 54–75. Facultad de Ciencias, Universidad Nacional de Colombia. | |
| dc.relation.references | Reyes, A., & Jaramillo, J. (2018). Symmetry and reversibility properties for quantum algebras and skew Poincaré–Birkhoff–Witt extensions. Ingeniería y Ciencia, 14(27), 29–52. | |
| dc.relation.references | Weibel, C. (1995). An introduction to homological algebra (Vol. 38). Cambridge University Press. | |
| dc.relation.references | Levasseur, T. (1992). Some properties of non-commutative regular graded rings. Glasgow Mathematical Journal, 34(3), 277–300. Cambridge University Press. | |
| dc.relation.references | Futorny, V., & Ovsienko, S. (2005). Kostant’s theorem for special filtered algebras. Bulletin of the London Mathematical Society, 37(2), 187–199. Cambridge University Press. | |
| dc.relation.references | Redman, I. T. (1996). The non-commutative algebraic geometry of some skew polynomial algebras (Tesis doctoral). University of Wisconsin–Milwaukee. | |
| dc.relation.references | Lezama, O. (2021). Some open problems in the context of skew PBW extensions and semi-graded rings. Communications in Mathematics and Statistics, 9(3), 347–378. | |
| dc.relation.references | Bell, A., & Goodearl, K. (1988). Uniform rank over differential operator rings and Poincaré–Birkhoff–Witt extensions. Pacific Journal of Mathematics, 131(1), 13–37. | |
| dc.relation.references | Ore, O. (1931). Linear equations in non-commutative fields. Annals of Mathematics, 32(3), 463–477. | |
| dc.relation.references | Ore, O. (1933). Theory of non-commutative polynomials. Annals of Mathematics, 34(3), 480–508. | |
| dc.relation.references | Nuss, P. (1991). L’homologie cyclique des algèbres enveloppantes des algèbres de Lie de dimension trois. Journal of Pure and Applied Algebra, 73(1), 39–71. | |
| dc.relation.references | Doran, B., Flajolet, P., Ismail, M., Lam, T. Y., & Lutwak, E. (2004). Categorical foundations: Special topics in order, topology, algebra, and sheaf theory (Vol. 97). Cambridge University Press. | |
| dc.relation.references | Knutson, A., Tao, T., & otros. (2003). Puzzles and (equivariant) cohomology of Grassmannians. Duke Mathematical Journal, 119(2), 221–260. | |
| dc.relation.references | Morandi, P. (1998). Examples of localization. Class Notes. | |
| dc.relation.references | Suárez, H., & Reyes, M. (2017). A generalized Koszul property for skew PBW extensions. Far East Journal of Mathematical Sciences, 101(2), 301–320. | |
| dc.relation.references | Artamonov, V., Lezama, O., & Fajardo, W. (2016). Extended modules and Ore extensions. Communications in Mathematics and Statistics, 4(2), 189–202. | |
| dc.relation.references | Zhang, J. (1997). A note on GK dimension of skew polynomial extensions. Proceedings of the American Mathematical Society, 125(2), 363–373. | |
| dc.relation.references | Zhang, J. J., & Zhang, J. (2008). Double Ore extensions. Journal of Pure and Applied Algebra, 212(12), 2668–2690. | |
| dc.relation.references | Dubois-Violette, M., Kerner, R., & Madore, J. (1990). Noncommutative differential geometry of matrix algebras. Journal of Mathematical Physics, 31(2), 316–322. | |
| dc.relation.references | Lee, J. M. (2006). Riemannian manifolds: An introduction to curvature (Vol. 176). Springer. | |
| dc.relation.references | Hong, J., & Kang, S. J. (2002). Introduction to quantum groups and crystal bases (Vol. 42). American Mathematical Society. | |
| dc.relation.references | Dubois-Violette, M. (1988). Dérivations et calcul différentiel non commutatif. Comptes Rendus de l’Académie des Sciences de Paris, Série I, 307, 403–408. | |
| dc.relation.references | Hochschild, G. (1942). Semi-simple algebras and generalized derivations. American Journal of Mathematics, 64(1), 677–694. | |
| dc.relation.references | Jacobson, N. (1937). Abstract derivation and Lie algebras. Transactions of the American Mathematical Society, 42(2), 206–224. | |
| dc.relation.references | Bell, A. D., & Smith, S. P. (1990). Some 3-dimensional skew polynomial rings. University of Wisconsin, Milwaukee (Preprint). | |
| dc.relation.references | Isaev, A. P., Pyatov, P. N., & Rittenberg, V. (2001). Diffusion algebras. Journal of Physics A, 34(29), 5815–5834. | |
| dc.relation.references | Jordan, D. A. (1993). Iterated skew polynomial rings and quantum groups. Journal of Algebra, 156(1), 194–218. | |
| dc.relation.references | Jordan, D. A. (2000). Down-up algebras and ambiskew polynomial rings. Journal of Algebra, 228(1), 311–346. | |
| dc.relation.references | Jordan, D. A., & Wells, I. (1996). Invariants for automorphisms of certain iterated skew polynomial rings. Proceedings of the Edinburgh Mathematical Society, 39(3), 461–472. | |
| dc.relation.references | Jordan, D. A., & Wells, I. (2013). Simple ambiskew polynomial rings. Journal of Algebra, 382, 46–70. | |
| dc.relation.references | Kandri-Rody, A., & Weispfenning, V. (1990). Non-commutative Gröbner bases in algebras of solvable type. Journal of Symbolic Computation, 9(1), 1–26. | |
| dc.relation.references | Bueso, J., Gómez-Torrecillas, J., & Verschoren, A. (2013). Algorithmic methods in non-commutative algebra: Applications to quantum groups (Vol. 17). Springer. | |
| dc.relation.references | Seiler, W. M. (2010). Involution: The formal theory of differential equations and its applications in computer algebra (Vol. 24). Springer. | |
| dc.relation.references | Le Bruyn, L., & Smith, S. P. (1993). Homogenized $\mathfrak{sl}_2$. Proceedings of the American Mathematical Society, 118(3), 725–730. | |
| dc.relation.references | Stafford, J. T. (1994). Regularity of algebras related to the Sklyanin algebra. Transactions of the American Mathematical Society, 341(2), 895–916. | |
| dc.relation.references | Vancliff, M. (1994). Quadratic algebras associated with the union of a quadric and a line in $\mathbb{P}^3$. Journal of Algebra, 165(1), 63–90. | |
| dc.relation.references | Shelton, B., & Vancliff, M. (1999). Embedding a quantum rank three quadric in a quantum $\mathbb{P}^3$. Communications in Algebra, 27(6), 2877–2904. | |
| dc.relation.references | Stephenson, D. R. (1996). Artin–Schelter regular algebras of global dimension three. Journal of Algebra, 183(1), 55–73. | |
| dc.relation.references | Cassidy, T., & Shelton, B. (2007). PBW-deformation theory and regular central extensions. Journal für die Reine und Angewandte Mathematik, 610, 1–12. | |
| dc.relation.references | Le Bruyn, L., Smith, S. P., & Van den Bergh, M. (1996). Central extensions of three-dimensional Artin–Schelter regular algebras. Mathematische Zeitschrift, 222(2), 171–212. | |
| dc.relation.references | Stephenson, D. R., & Vancliff, M. (2006). Some finite quantum $\mathbb{P}^3$s that are infinite modules over their centers. Journal of Algebra, 297(1), 208–215. | |
| dc.relation.references | Van Rompay, K., & Vancliff, M. (2000). Four-dimensional regular algebras with point scheme a nonsingular quadric in $\mathbb{P}^3$. Communications in Algebra, 28(5), 2211–2242. | |
| dc.relation.references | Van Rompay, K., Vancliff, M., & Willaert, L. (1998). Some quantum $\mathbb{P}^3$ with finitely many points. Communications in Algebra, 26(4), 1193–1208. | |
| dc.relation.references | Gaddis, J. D. (2013). PBW deformations of Artin–Schelter regular algebras and their homogenizations (Tesis doctoral). University of Wisconsin–Milwaukee. | |
| dc.relation.references | Gaddis, J. D. (2015). Two-generated algebras and standard-form congruence. Communications in Algebra, 43(4), 1668–1686. | |
| dc.relation.references | Gaddis, J. D. (2016). PBW deformations of Artin–Schelter regular algebras. Journal of Algebra and Its Applications, 15(4), 1650064. | |
| dc.relation.references | Lu, D. M., & Zhou, G. S. (2014). Artin–Schelter regular algebras of dimension five with two generators. Journal of Pure and Applied Algebra, 218(5), 937–961. | |
| dc.relation.references | Lu, D. M., Shen, G., & Zhou, G. S. (2015). Homogeneous PBW deformation for Artin–Schelter regular algebras. Bulletin of the Australian Mathematical Society, 91(1), 53–68. | |
| dc.relation.references | Gurevich, D. (1986). The Yang–Baxter equation and the generalization of formal Lie theory. Doklady Akademii Nauk SSSR, 288(4), 797–801. | |
| dc.relation.references | Demidov, E., Manin, Y., Mukhin, E., & Zhdanovich, D. (1990). Non-standard quantum deformations of GL(n) and constant solutions of the Yang–Baxter equation. Progress of Theoretical Physics Supplement, 102, 203–218. | |
| dc.relation.references | Suárez, H., Lezama, O., & Reyes, A. (2015). Some relations between N-Koszul, Artin–Schelter regular and Calabi–Yau with skew PBW extensions. Ciencia en Desarrollo, 6(2), 205–213. | |
| dc.relation.references | Liu, L., Wang, S., & Wu, Q. (2014). Twisted Calabi–Yau property of Ore extensions. Journal of Noncommutative Geometry, 8(12), 587–609. | |
| dc.relation.references | Mansour, T., & Schork, M. (2016). Commutation relations, normal ordering, and Stirling numbers. CRC Press. | |
| dc.relation.references | Dirac, P. A. M. (1926). On quantum algebra. Mathematical Proceedings of the Cambridge Philosophical Society, 23, 412–418. | |
| dc.relation.references | Reyes, A., & Rodríguez, C. (2021). The McCoy condition on skew Poincaré–Birkhoff–Witt extensions. Communications in Mathematics and Statistics, 9(1), 1–21. | |
| dc.relation.references | Dirac, P. A. M. (1926). Quantum mechanics and a preliminary investigation of the hydrogen atom. Proceedings of the Royal Society of London. Series A, 110, 561–579. | |
| dc.relation.references | McCoy, N. H. (1929). On commutation formulas in the algebra of quantum mechanics. Transactions of the American Mathematical Society, 31, 793–806. | |
| dc.relation.references | Maslov, V. P. (1978). Application of the method of ordered operators to obtain exact solutions. Theoretical and Mathematical Physics, 33, 960–976. | |
| dc.relation.references | Littlewood, D. E. (1933). On the classification of algebras. Proceedings of the London Mathematical Society, 35, 200–240. | |
| dc.relation.references | Díaz, R., & Pariguan, E. (2005). Quantum symmetric functions. Communications in Algebra, 33, 1947–1978. | |
| dc.relation.references | Díaz, R., & Pariguan, E. (2009). On the q-meromorphic Weyl algebra. São Paulo Journal of Mathematical Sciences, 3(2), 281–296. | |
| dc.relation.references | Beggs, E. J., & Majid, S. (2020). Quantum Riemannian geometry (Vol. 355). Springer Cham. | |
| dc.relation.references | Goodearl, K. R., & Letzter, E. S. (1994). Prime ideals in skew and q-skew polynomial rings (Vol. 109). American Mathematical Society. | |
| dc.relation.references | Manin, Y. I. (2018). Quantum groups and noncommutative geometry. With a contribution by Theo Raedschelders and Michel Van den Bergh. Springer Cham. | |
| dc.relation.references | Berger, M. (2003). A panoramic view of Riemannian geometry. Springer Berlin, Heidelberg. | |
| dc.relation.references | Dăscălescu, S., Năstăsescu, C., & Raianu, Ş. (2001). Hopf algebras: An introduction (Vol. 235). Marcel Dekker. | |
| dc.relation.references | Carvalho, P. A. A. B., Lopes, S. A., & Matczuk, J. (2011). Double Ore extensions versus iterated Ore extensions. Communications in Algebra, 39(8), 2838–2848. | |
| dc.relation.references | Díaz, R., & Pariguan, E. (2009). On the q-meromorphic Weyl algebra. São Paulo Journal of Mathematical Sciences, 3(2), 283–298. | |
| dc.relation.references | Giaquinto, A., & Zhang, J. J. (1995). Quantum Weyl algebras. Journal of Algebra, 176(3), 861–881. | |
| dc.relation.references | Coutinho, S. C. (1995). A primer of algebraic D-modules. Cambridge University Press. | |
| dc.relation.references | Lopes, S. (2024). Noncommutative algebra and representation theory: Symmetry, structure & invariants. Communications in Mathematics, 32(3), 63–117. | |
| dc.relation.references | Li, H. (2002). Noncommutative Gröbner bases and filtered-graded transfer. Springer Berlin, Heidelberg. https://doi.org/10.1007/b84211 | |
| dc.relation.references | Jannussis, A., Brodimas, G., & Sourlas, D. (1981). Remarks on the q-quantization. Lettere al Nuovo Cimento, 30, 123–127. | |
| dc.relation.references | Kuryshkin, M. V. (1980). Opérateurs quantiques généralisés de création et d’annihilation. Annales de la Fondation Louis de Broglie, 5, 111–125. | |
| dc.relation.references | Shirikov, E. N. (2005). Two-generated graded algebras. Algebra and Discrete Mathematics, 4(3), 60–84. | |
| dc.relation.references | Shirikov, E. N. (2008). Jordanian plane. Journal of Mathematical Sciences (New York), 154(2), 270–278. | |
| dc.relation.references | Shirikov, E. N. (2007). The Jordanian plane over a field of positive characteristic. Mathematical Notes, 82, 238–256. | |
| dc.relation.references | Shirikov, E. N. (2009). Irreducible modules over a Jordanian plane over a field of characteristic zero. Moscow University Mathematics Bulletin, 64, 47–50. | |
| dc.relation.references | Isaev, A. P., Pyatov, P. N., & Rittenberg, V. (2001). Diffusion algebras. Journal of Physics A, 34(29), 5815–5834. | |
| dc.relation.references | Benkart, G., & Roby, T. (1998). Down–up algebras. Journal of Algebra, 209(1), 305–344. | |
| dc.relation.references | Smith, S. P. (1992). Quantum groups: An introduction and survey for ring theorists. In S. Montgomery & L. Small (Eds.), Noncommutative rings (pp. 131–178). Springer-Verlag. | |
| dc.relation.references | Jategaonkar, V. A. (1984). A multiplicative analogue of the Weyl algebra. Communications in Algebra, 12(14), 1669–1688. | |
| dc.relation.references | Venegas, C. (2015). Automorphisms for skew PBW extensions and skew quantum polynomial rings. Communications in Algebra, 43(5), 1877–1897. | |
| dc.relation.references | Wess, J., & Zumino, B. (1991). Covariant differential calculus on the quantum hyperplane. Nuclear Physics B – Proceedings Supplements, 18(2), 302–312. | |
| dc.relation.references | Witten, E. (1990). Gauge theories, vertex models, and quantum groups. Nuclear Physics B, 330(2–3), 285–346. | |
| dc.relation.references | Witten, E. (1991). Quantization of Chern–Simons gauge theory with complex gauge group. Communications in Mathematical Physics, 137(1), 29–66. | |
| dc.relation.references | Woronowicz, S. L. (1987). Twisted SU(2)-group, an example of a non-commutative differential calculus. Publications of the Research Institute for Mathematical Sciences, 23, 117–181. | |
| dc.relation.references | Passman, D. S. (1987). Prime ideals in enveloping rings. Transactions of the American Mathematical Society, 302(2), 535–560. | |
| dc.relation.references | Pusz, W., & Woronowicz, S. L. (1989). Twisted second quantization. Reports on Mathematical Physics, 27(2), 231–257. | |
| dc.relation.references | Kirkman, E., Musson, I. M., & Passman, D. S. (1999). Noetherian down-up algebras. Proceedings of the American Mathematical Society, 127(11), 3161–3167. | |
| dc.relation.references | Le Bruyn, L. (1994). Two remarks on Witten’s quantum enveloping algebra. Communications in Algebra, 22(3), 865–876. | |
| dc.relation.references | Le Bruyn, L. (1995). Conformal sl₂ enveloping algebras. Communications in Algebra, 23(4), 1325–1362. | |
| dc.relation.references | Kulkarni, R. S. (1999). Irreducible representations of Witten’s deformations of U(sl₂). Journal of Algebra, 214(1), 64–91. | |
| dc.relation.references | Cohn, P. M. (1985). Free rings and their relations (Vol. 2). Academic Press. | |
| dc.relation.references | Rosenberg, A. (1995). Noncommutative algebraic geometry and representations of quantized algebras (Vol. 330). Kluwer Academic Publishers. | |
| dc.relation.references | Redman, I. T. (1999). The homogenization of the three dimensional skew polynomial algebras of type I. Communications in Algebra, 27(11), 5587–5602. | |
| dc.relation.references | Iyudu, N. (2014). Representation spaces of the Jordanian plane. Communications in Algebra, 42(8), 3507–3540. | |
| dc.relation.references | Reca, S., & Solotar, A. (2018). Homological invariants relating the super Jordanian plane to the Virasoro algebra. Journal of Algebra, 507, 120–185. | |
| dc.relation.references | Brzeziński, T. (2008). Non-commutative connections of the second kind. Journal of Algebra and Its Applications, 7(5), 557–573. | |
| dc.relation.references | Penkov, I. B. (1983). D-modules on supermanifolds. Inventiones Mathematicae, 71, 501–512. | |
| dc.relation.references | Vinogradov, M. M. (1995). Coconnections and integral forms. Doklady Mathematics, 50(2), 229–233. | |
| dc.relation.references | Yuri, M. (1988). Gauge field theory and complex geometry. Springer-Verlag. | |
| dc.relation.references | Verbovetsky, A. (1997). Differential operators over quantum spaces. Acta Applicandae Mathematicae, 49, 339–361. | |
| dc.relation.references | Grothendieck, A. (1964). Éléments de géométrie algébrique IV. Étude locale des schémas et des morphismes de schémas (Vol. 20). Publications Mathématiques de l’IHÉS. | |
| dc.relation.references | Schelter, W. F. (1986). Smooth algebras. Journal of Algebra, 103(2), 677–685. | |
| dc.relation.references | Cuntz, J., & Quillen, D. (1995). Algebra extensions and nonsingularity. Journal of the American Mathematical Society, 8(2), 251–289. | |
| dc.relation.references | Van den Bergh, M. (1998). A relation between Hochschild homology and cohomology for Gorenstein rings. Proceedings of the American Mathematical Society, 126, 1345–1348. (Erratum 2002, Proceedings of the American Mathematical Society, 130, 2809–2810). | |
| dc.relation.references | Brzeziński, T. (2016). Noncommutative differential geometry of generalized Weyl algebras. SIGMA – Symmetry, Integrability and Geometry: Methods and Applications, 12, 059. | |
| dc.relation.references | Brzeziński, T., & Szymański. (2018). The C*-algebras of quantum lens and weighted projective spaces. Journal of Noncommutative Geometry, 12(1), 195–215. | |
| dc.relation.references | Zhang, J. J., & Zhang, J. (2009). Double extension regular algebras of type (14641). Journal of Algebra, 322, 373–409. | |
| dc.relation.references | Kirkman, E., Procesi, C., & Small, L. (1994). A q-analog for the Virasoro algebra. Communications in Algebra, 22(10), 3755–3774. | |
| dc.relation.references | Reyes, A., & Suárez, Y. (2018). On the ACCP in skew Poincaré–Birkhoff–Witt extensions. Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry, 59(4), 625–643. | |
| dc.relation.references | Launois, S., & Lenagan, T. H. (2013). Automorphisms of quantum matrices. Glasgow Mathematical Journal, 55(A), 89–100. | |
| dc.relation.references | Launois, S., & Lenagan, T. H. (2007). Primitive ideals and automorphisms of quantum matrices. Algebras and Representation Theory, 10(4), 339–365. | |
| dc.relation.references | Yakimov, M. (2013). The Launois–Lenagan conjecture. Journal of Algebra, 392, 1–9. | |
| dc.relation.references | Gómez, J., & Suárez, H. (2018). Some homological properties of Jordan plane. Ciencia en Desarrollo, 9(2), 69–82. | |
| dc.relation.references | Zharinov, V. V. (1999). On derivations of the Heisenberg algebra. Theoretical and Mathematical Physics, 118(2), 129–151. | |
| dc.relation.references | Rimmer, M. (1978). Isomorphisms between skew polynomial rings. Journal of the Australian Mathematical Society, 25(3), 314–321. | |
| dc.relation.references | Benkart, G., & Roby, T. (1998). Down–up algebras. Journal of Algebra, 209(1), 305–344. | |
| dc.relation.references | Yekutieli, A., & Zhang, J. J. (1997). Serre duality for noncommutative projective schemes. Proceedings of the American Mathematical Society, 125(3), 697–707. | |
| dc.relation.references | Artin, M., & Zhang, J. J. (1994). Noncommutative projective schemes. Advances in Mathematics, 109(2), 228–287. | |
| dc.relation.references | Gelfand, I. M., & Kirillov, A. A. (1966). On fields connected with the enveloping algebras of Lie algebras. Doklady Akademii Nauk, 167(3), 503–505. | |
| dc.relation.references | Gelfand, I. M., & Kirillov, A. A. (1966). Sur les corps liés aux algèbres enveloppantes des algèbres de Lie. Publications Mathématiques de l’IHÉS, 31, 5–19. | |
| dc.relation.references | Krause, G. R., & Lenagan, T. H. (2000). Growth of algebras and Gelfand-Kirillov dimension (Rev. ed., Graduate Studies in Mathematics, Vol. 22). American Mathematical Society. | |
| dc.rights.accessrights | info:eu-repo/semantics/openAccess | |
| dc.rights.license | Reconocimiento 4.0 Internacional | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject.lemb | Geometría diferencial | spa |
| dc.subject.lemb | Geometry, differential | eng |
| dc.subject.lemb | Álgebras de funciones | spa |
| dc.subject.lemb | Function algebras | eng |
| dc.subject.lemb | Análisis matemático | spa |
| dc.subject.lemb | Mathematical analysis | eng |
| dc.subject.proposal | Noncommutative differential geometry | eng |
| dc.subject.proposal | Smooth geometry | eng |
| dc.subject.proposal | Differential smoothness | eng |
| dc.subject.proposal | Differential calculus | eng |
| dc.subject.proposal | Integrable calculus | eng |
| dc.subject.proposal | Artin-Schelter regular algebra | eng |
| dc.subject.proposal | Noncommutative projective space | eng |
| dc.subject.proposal | Semi-graded ring | eng |
| dc.subject.proposal | Serre duality | eng |
| dc.subject.proposal | Geometría diferencial no conmutativa | spa |
| dc.subject.proposal | Geometría suave | spa |
| dc.subject.proposal | Suavidad diferencial | spa |
| dc.subject.proposal | Cálculo diferencial | spa |
| dc.subject.proposal | Cálculo integral | spa |
| dc.subject.proposal | Álgebra regular Artin-Schelter | spa |
| dc.subject.proposal | Espacio proyectivo no conmutativo | spa |
| dc.subject.proposal | Anillo semi-graduado | spa |
| dc.subject.proposal | Dalidad de Serre | spa |
| dc.title | On the noncommutative differential geometry of semi-graded Artin-Schelter regular algebras | eng |
| dc.title.translated | Sobre la geometría diferencial no conmutativa de las álgebras semigraduadas Artin-Schelter regulares | spa |
| dc.type | Trabajo de grado - Doctorado | |
| dc.type.coar | http://purl.org/coar/resource_type/c_db06 | |
| dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | |
| dc.type.content | Text | |
| dc.type.driver | info:eu-repo/semantics/doctoralThesis | |
| dc.type.redcol | http://purl.org/redcol/resource_type/TD | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dcterms.audience.professionaldevelopment | Investigadores | |
| dcterms.audience.professionaldevelopment | Estudiantes | |
| dcterms.audience.professionaldevelopment | Maestros | |
| oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |
Archivos
Bloque original
1 - 1 de 1
Cargando...
- Nombre:
- On the noncommutative differential geometry of semi-graded Artin-Schelter regular algebras.pdf
- Tamaño:
- 1.62 MB
- Formato:
- Adobe Portable Document Format
Bloque de licencias
1 - 1 de 1
Cargando...
- Nombre:
- license.txt
- Tamaño:
- 5.74 KB
- Formato:
- Item-specific license agreed upon to submission
- Descripción: