Gröbner-Shirshov bases for Sklyanin algebras

In this thesis we study the theory of Gröbner-Shirshov bases for three- dimensional and four-dimensional Sklyanin algebras. First, we present a brief construction of free algebras, and then describe the theory of Gröbner-Shirshov bases of these algebras. In addition, we present examples on the compu...

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Autores:: Herrera Cano, Karol Stefany

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Fecha de publicación:: 2024

Institución:: Universidad Nacional de Colombia

Repositorio:: Universidad Nacional de Colombia

Idioma:: eng

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dc.title.eng.fl_str_mv	Gröbner-Shirshov bases for Sklyanin algebras
dc.title.translated.spa.fl_str_mv	Bases de Gröbner-Shirshov para álgebras de Sklyanin
title	Gröbner-Shirshov bases for Sklyanin algebras
spellingShingle	Gröbner-Shirshov bases for Sklyanin algebras Base de Gröbner-Shirshov Algoritmo de Shirshov Lema del diamante Álgebra PBW Álgebra de Sklyanin Gröbner-Shirshov basis Shirshov's algorithm Diamond lemma PBW algebra Sklyanin algebra
title_short	Gröbner-Shirshov bases for Sklyanin algebras
title_full	Gröbner-Shirshov bases for Sklyanin algebras
title_fullStr	Gröbner-Shirshov bases for Sklyanin algebras
title_full_unstemmed	Gröbner-Shirshov bases for Sklyanin algebras
title_sort	Gröbner-Shirshov bases for Sklyanin algebras
dc.creator.fl_str_mv	Herrera Cano, Karol Stefany
dc.contributor.advisor.none.fl_str_mv	Reyes Villamil, Milton Armando
dc.contributor.author.none.fl_str_mv	Herrera Cano, Karol Stefany
dc.subject.proposal.spa.fl_str_mv	Base de Gröbner-Shirshov Algoritmo de Shirshov Lema del diamante Álgebra PBW Álgebra de Sklyanin
topic	Base de Gröbner-Shirshov Algoritmo de Shirshov Lema del diamante Álgebra PBW Álgebra de Sklyanin Gröbner-Shirshov basis Shirshov's algorithm Diamond lemma PBW algebra Sklyanin algebra
dc.subject.proposal.eng.fl_str_mv	Gröbner-Shirshov basis Shirshov's algorithm Diamond lemma PBW algebra Sklyanin algebra
description	In this thesis we study the theory of Gröbner-Shirshov bases for three- dimensional and four-dimensional Sklyanin algebras. First, we present a brief construction of free algebras, and then describe the theory of Gröbner-Shirshov bases of these algebras. In addition, we present examples on the computation of the bases, and in particular, we consider some relations with PBW algebras. Next, we address the origin and review some of the properties of three-dimensional Sklyanin algebras, especially the PBW property. With this, we classify the three-dimensional Sklyanin algebras that are or not PBW algebras into at least eight families, and we compute their Gröbner-Shirshov bases, obtaining in some cases finite bases and in others, apparently infinite ones. In the same way, we study four-dimensional Sklyanin algebras, reviewing some of their algebraic properties, their classification into six families of degenerate algebras, and we compute their Gröbner-Shirshov bases obtaining only for one family, a finite basis. Finally, we use a code developed in MATLAB to review the hand-made computations of the Gröbner-Shirshov bases in the different families of the three-dimensional Sklyanin algebras, and at the same time test the correctness of the code. Once verified, we use it to perform the calculations for four-dimensional Sklyanin algebras
publishDate	2024
dc.date.accessioned.none.fl_str_mv	2024-05-14T16:33:38Z
dc.date.available.none.fl_str_mv	2024-05-14T16:33:38Z
dc.date.issued.none.fl_str_mv	2024
dc.type.spa.fl_str_mv	Trabajo de grado - Maestría
dc.type.driver.spa.fl_str_mv	info:eu-repo/semantics/masterThesis
dc.type.version.spa.fl_str_mv	info:eu-repo/semantics/acceptedVersion
dc.type.content.spa.fl_str_mv	Text
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status_str	acceptedVersion
dc.identifier.uri.none.fl_str_mv	https://repositorio.unal.edu.co/handle/unal/86074
dc.identifier.instname.spa.fl_str_mv	Universidad Nacional de Colombia
dc.identifier.reponame.spa.fl_str_mv	Repositorio Institucional Universidad Nacional de Colombia
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.unal.edu.co/
url	https://repositorio.unal.edu.co/handle/unal/86074 https://repositorio.unal.edu.co/
identifier_str_mv	Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia
dc.language.iso.spa.fl_str_mv	eng
language	eng
dc.relation.references.spa.fl_str_mv	J. Apel. Gröbnerbasen in Nichtkommutativen Algebren und ihre Anwendung. PhD thesis, Universität Leipzig, 1988. M. Artin and W. Schelter. Graded algebras of global dimension 3. Adv. in Math., 66(2):171–216, 1987 M. Artin, J. Tate, and M. Van den Bergh. Some Algebras Associated to Automorphisms of Elliptic Curves. In The Grothendieck Festschrift, pages 33–85. Springer, 1990. M. Artin, J. Tate, and M. Van den Bergh. Modules over regular algebras of dimension 3. Invent. Math., 106(2):335–388, 1991 V. V. Bavula. Description of bi-quadratic algebras on 3 generators with PBW basis. J. Algebra, 631:695–730, 2023. L. Bokut and Y. Chen. Gröbner-Shirshov bases and their calculation. Bull. Math. Sci., 4(3):325–395, 2014. L. Bokut and Y. Chen. Gröbner-Shirshov bases theory and Shirshov algorithm. Novosibirsk: RIZ NSU, 2014. Y. Bai and Y. Chen. Gröbner-Shirshov bases theory for Leibniz superalgebras. Comm. Algebra, 50(8):3524–3542, 2022 Y. Bai, Y. Chen, and Z. Zhang. Gelfand-Kirillov dimension of bicommutative algebras. Linear Multilinear Algebra, 70(22):7623–7649, 2021 G. M. Bergman. The Diamond lemma for ring theory. Adv. Math., 29(2):178–218, 1978 L. Bokut, Y. Fong, and W.F. Ke. Gröbner-Shirshov bases and composition lemma for associative conformal algebras: an example. Contemp. Math., 264:63–90, 2000. A. Bell and K. Goodearl. Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions. Pacific J. Math., 131(1):13–37, 1988 J. Bueso, J. Gómez-Torrecillas, and A. Verschoren. Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups. Mathematical Modelling: Theory and Applications, Springer, 2003. L. Bokut and P. Malcolmson. Gröbner-Shirshov bases for quantum enveloping algebras. Israel J. Math., 96:97–113, 1996 L. Bokut and L. Makar-Limanov. A basis of a free metabelian associative algebra. Sib. Math. J., 32(6):910–915, 1991 L. Bokut. Unsolvability of the equality problem and subalgebras of finitely presented Lie algebras. Izv. Ross. Akad. Nauk Ser. Mat., 36(6):1173–1219, 1972. L. Bokut. Embeddings into simple associative algebras. Algebra Logika, 15(2):117–142, 1976 G. Bellamy, D. Rogalski, T. Schedler, J. Stafford, and M. Wemyss. Noncom- mutative Algebraic Geometry, volume 64. Cambridge University Press, 2016. A. D. Bell and S. P. Smith. Some 3-dimensional skew polynomial rings. University of Wisconsin, Milwaukee, preprint, 1990. B. Buchberger. An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal (PhD thesis in German). Institute University of Innsbruck, 1965 B. Buchberger. An algorithmical criteria for the solvability of algebraic systems of equations. Aequationes Math, 4:374–383, 1970 I. V. Cherednik. On R-matrix quantization of formal loop groups. Group theoretical methods in physics, 2:161–180, 1986. A. Chirvasitu and S. P. Smith. Some algebras having relations like those for the 4-dimensional Sklyanin algebras. J. Korean Math. Soc., 60(4):745–777, 2023. T. Cassidy and M. Vancliff. Generalizations of Graded Clifford Algebras and of Complete Intersections. J. Lond. Math. Soc., 81(1):91–112, 2010. V. G. Drinfeld. Quantum Groups. Zapiski Nauchnykh Seminarov POMI, 155:18– 49, 1986. W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suárez, and H. Venegas. Skew PBW Extensions. Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications. Springer, Cham, 2020. B. L. Feigin and A. V. Odesskii. Sklyanin algebras associated with an elliptic curve. Preprint deposited with Institute of Theoretical Physics of the Academy of Sciences of the Ukrainian SSR, page 33, 1989. B. L. Feigin and A. V. Odesskii. Sklyanin elliptic algebras. Funct. Anal. Appl., 23(3):207–214, 1989 A. V. Golovashkin and V. M. Maksimov. Skew Ore polynomials of higher orders generated by homogeneous quadratic relations. Russian Math. Surveys, 53(2):384–386, 1998. E. L. Green. Noncommutative Gröbner bases, and projective resolutions. In Computational Methods for Representations of Groups and Algebras: Euroconference in Essen (Germany), April 1–5, 1977, pages 29–60. Springer, 1999. P. P. Grivel. Une histoire du théorème de Poincare-Birkhoff-Witt. Expo. Math., 22(2):145–184, 2004. K. R. Goodearl and R. B. Warfield. An Introduction to Noncommutative Noetherian Rings. Cambridge University Press. London, 2004. J. Huang and Y. Chen. Gröbner- Shirshov Bases Theory for Trialgebras. Mathematics, 9(11):1207, 2021 A. P. Isaev, P. N. Pyatov, and V. Rittenberg. Diffusion algebras. J. Phys. A., 34(29):5815–5834, 2001. N. Iyudu and S. Shkarin. Three dimensional Sklyanin algebras and Gröbner bases. J. Algebra, 470:379–419, 2017. J. C. Jantzen. Lectures on Quantum Groups, volume 6. American Mathematical Soc., 1996. E. G. Karpuz, F. Ateş, and A.S. Çevik. Gröbner-Shirshov bases of some Weyl groups. Rocky Mountain J. Math, 2015. A. Kandri-Rody and V. Weispfenning. Non-commutative Gröbner Bases in Algebras of Solvable Type. J. Symbolic Computation, 9(1):1–26, 1990. V. Levandovskyy. Non-commutative Computer Algebra for polynomial algebras: Gröbner bases, applications and implementation. PhD thesis, Technische Univer- sität Kaiserslautern, 2005. O. Lezama. Cuadernos de Álgebra: Anillos y Módulos, volume 2. Universidad Nacional de Colombia, Bogotá, D. C., 2023. H. Li. Noncommutative Gröbner Bases and Filtered-Graded Transfer. Lecture Notes in Mathematics, LNM, volume 1795, Springer, 2002. Y. Li, Q. Mo, and L. Bokut. Gröbner-Shirshov bases for symmetric brace algebras. Comm. Algebra, 49(2):892–904, 2020 T. Mora. An Introduction to Commutative and Noncommutative Gröbner bases. Theoret. Comput. Sci., 134(1):131–173, 1994. M. H. A. Newman. On theories with a combinatorial definition of “equiva- lence”. Ann. Math, pages 223–243, 1942. A. Niño and A. Reyes. On centralizers and pseudo-multidegree functions for non-commutative rings having PBW bases. J. Algebra Appl., https://doi. org/10.1142/S0219498825501099, 2023. A. Niño, M. C. Ramírez, and A. Reyes. A first approach to the Burchnall- Chaundy theory for quadratic algebras having PBW bases. https://arxiv. org/abs/2401.10023, 2023. O. Ore. Linear Equations in Non-commutative Fields. Ann. of Math. (2), 32(3):463–477, 1931. O. Ore. Theory of Non-commutative Polynomials. Ann. of Math. (2), 34(3):480– 508, 1933. A. Polishchuk and L. Positselski. Quadratic algebras, volume 37. University Lecture Series. American Mathematical Soc., 2005. I. T. Redman. The Non-Commutative Algebraic Geometry of some Skew Polynomial Algebras. PhD thesis, University of Wisconsin - Milwaukee, 1996. I. T. Redman. The homogenization of the three dimensional skew polynomial algebras of type I. Comm. Algebra, 27(11):5587–5602, 1999. D. Rogalski. Artin-Schelter Regular Algebras. https://arxiv.org/pdf/2307.03174v1.pdf, 2023. J. J. Rotman. Advanced Modern Algebra. Second Edition, volume 114. Graduate Studies in Mathematics. Springer, 2010. A. Reyes and H. Suárez. Bases for Quantum Algebras and Skew Poincaré- Birkhoff-Witt extensions. Momento, 54(1):54–75, 2017. A. Reyes and C. Sarmiento. On the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras. Internat. J. Algebra Comput., 32(03):529–559, 2022. K. Saito. Extended affine root systems i (Coxeter transformations). Publ. Res. Inst. Math. Sci., 21(1):75–179, 1985. W. M. Seiler. Involution. The Formal Theory of Differential Equations and its Applications in Computer Algebra, volume 24. Algorithms and Computation in Mathematics (AACIM). Springer Berlin, Heidelberg, 2010. A. I. Shirshov. On free Lie rings, volume 87. Russian Academy of Sciences, Steklov Mathematical Institute of Russian, 1958. A. I. Shirshov. Some algorithmic problems for Lie algebras. Springer, 1962. E. K. Sklyanin. Some algebraic structures connected with the Yang-Baxter equation. Funct. Anal. Appl., 16(4):263–270, 1982. E. K. Sklyanin. Some algebraic structures connected with the Yang-Baxter equation. Representations of Quantum algebras. Funct. Anal. Appl., 17(4):273– 284, 1983. S. P. Smith. “Degenerate” 3-dimensional Sklyanin algebras are monomial algebras. J. Algebra, 358:74–86, 2012. S. P. Smith and J. T. Stafford. Regularity of the four dimensional Sklyanin algebra. Compos. Math., 83(3):259–289, 1992. K. Saito and T. Takebayashi. Extended affine root systems III (elliptic Weyl groups). Publ. Res. Inst. Math. Sci., 33(2):301–329, 1997. J. T. Stafford. Regularity of algebras related to the Sklyanin algebra. Trans. Amer. Math. Soc., 341(2):895–916, 1994. D. R. Stephenson. Artin-Schelter Regular Algebras of Global Dimension Three. J. Algebra, 183(1):55–73, 1996. B. Shelton and M. Vancliff. Embedding a quantum rank three quadric in a quantum P3. Comm. Algebra, 27(6):2877–2904, 1999. D. R. Stephenson and M. Vancliff. Some finite quantum P3s that are infinite modules over their centers. J. Algebra, 297(1):208–215, 2006. M. Vancliff. Quadratic algebras associated with the union of a quadric and a line in P3. J. Algebra, 165(1):63–90, 1994. K. Van Rompay and M. Vancliff. Four-dimensional regular algebras with point scheme a nonsingular quadric in P3. Comm. Algebra, 28(5):2211–2242, 2000. K. Van Rompay, M. Vancliff, and L. Willaert. Some quantum P3 with finitely many points. Comm. Algebra, 26(4):1193–1208, 1998. M. Vancliff and K. Van Rompay. Embedding a Quantum Nonsingular Quadric in a Quantum P3. J. Algebra, 195(1):93–129, 1997. C. Walton. Degenerate Sklyanin algebras and generalized twisted homogeneous coordinate rings. J. Algebra, 322(7):2508–2527, 2009. X. Xiu. Non-commutative Gröbner bases and applications. PhD thesis, Universität Passau, 2012. G. Yunus, Z. Gao, and A. Obul. Gröbner-Shirshov basis of quantum groups. 22(03):495–516, 2015. G. Yunus and A. Obul. Gröbner-Shirshov basis of quantum group of type D4. Chinese Ann. Math., Ser. B, 32(4):581–592, 2011. Z. Zhang, Y Chen, and Bokut. L. Word problem for finitely presented metabelian Poisson algebras. arXiv: Rings and Algebras, 2019. X. Zhao. Jacobson’s Lemma via Gröbner-Shirshov Bases. Algebra Colloq., 24(02):309–314, 2017. J. J. Zhang and J. Zhang. Double Ore extensions. J. Pure Appl. Algebra, 212(12):2668–2690, 2008. J. J. Zhang and J. Zhang. Double extension regular algebras of type (14641). J. Algebra, 322(2):373–409, 2009. A. I. Shirshov. Some algorithmic problems for $\varepsilon$-algebras. Springer, 1962. Y. Ren and A. Obul. Gröbner-Shirshov basis of quantum group of type ${G}_2$. Comm. Algebra, 39(5):1510–1518, 2011. C. Qiang and A. Obul. The Skew-commutator Relations and Gröbner-Shirshov Bases of Quantum Group of Type ${C}_3$. Acta Math. Appl. Sin. Engl. Ser., 36(4):825–835, 2020. L. Le Bruyn and S. P. Smith. Homogenized $\mathfrak{sl}_2$. Proc. Amer. Math. Soc., 118(3):725–730, 1993. M. Jimbo. A $q$-difference analogue of ${U}(\mathfrak{g})$ and the Yang-Baxter equation. Lett. Math. Phys., 10:63–69, 1985.
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dc.publisher.spa.fl_str_mv	Universidad Nacional de Colombia
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spelling	Reconocimiento 4.0 Internacionalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Reyes Villamil, Milton Armando767f31307c790697ee2bf5d2c4f57583Herrera Cano, Karol Stefanydd23dcd874fb16f4ca71319624523aa52024-05-14T16:33:38Z2024-05-14T16:33:38Z2024https://repositorio.unal.edu.co/handle/unal/86074Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/In this thesis we study the theory of Gröbner-Shirshov bases for three- dimensional and four-dimensional Sklyanin algebras. First, we present a brief construction of free algebras, and then describe the theory of Gröbner-Shirshov bases of these algebras. In addition, we present examples on the computation of the bases, and in particular, we consider some relations with PBW algebras. Next, we address the origin and review some of the properties of three-dimensional Sklyanin algebras, especially the PBW property. With this, we classify the three-dimensional Sklyanin algebras that are or not PBW algebras into at least eight families, and we compute their Gröbner-Shirshov bases, obtaining in some cases finite bases and in others, apparently infinite ones. In the same way, we study four-dimensional Sklyanin algebras, reviewing some of their algebraic properties, their classification into six families of degenerate algebras, and we compute their Gröbner-Shirshov bases obtaining only for one family, a finite basis. Finally, we use a code developed in MATLAB to review the hand-made computations of the Gröbner-Shirshov bases in the different families of the three-dimensional Sklyanin algebras, and at the same time test the correctness of the code. Once verified, we use it to perform the calculations for four-dimensional Sklyanin algebrasEn esta tesis estudiamos la teoría de bases de Gröbner-Shirshov para las álgebras de Sklyanin tridimensionales y cuatrodimensionales. En primer lugar, presentamos una breve construcción de las álgebras libres, para luego describir la teoría de bases de Gröbner- Shirshov de estas álgebras. Además, presentamos ejemplos sobre el cálculo de dichas bases, y en particular, conectamos estas bases con las álgebras PBW. Luego, abordamos el origen y revisamos algunas de las propiedades sobre las álgebras de Sklyanin tridimensionales, en especial, la propiedad PBW. Gracias a esta, clasificamos en al menos ocho familias las álgebras de Sklyanin tridimensionales que son o no son álgebras PBW, y calculamos sus bases de Gröbner-Shirshov, obteniendo en algunos casos bases finitas y en otros, al parecer, infinitas. De la misma manera, estudiamos las álgebras de Sklyanin cuatrodimensionales, revisando algunas de sus propiedades algebraicas y las clasificamos en seis familias de álgebras degeneradas, y calculamos sus bases de Gröbner-Shirshov obteniendo solo para una familia, una base finita. Finalmente, utilizamos un código hecho en MATLAB para revisar los cálculos hechos a mano de las bases de Gröbner-Shirshov en las diferentes familias de las álgebras de Sklyanin tridimensionales, y al mismo tiempo probar la veracidad del código. Una vez comprobado, lo usamos para realizar los cálculos para álgebras de Sklyanin cuatrodimensionales (Texto tomado de la fuente)Maestríavi, 189 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede BogotáGröbner-Shirshov bases for Sklyanin algebrasBases de Gröbner-Shirshov para álgebras de SklyaninTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMJ. Apel. Gröbnerbasen in Nichtkommutativen Algebren und ihre Anwendung. PhD thesis, Universität Leipzig, 1988.M. Artin and W. Schelter. Graded algebras of global dimension 3. Adv. in Math., 66(2):171–216, 1987M. Artin, J. Tate, and M. Van den Bergh. Some Algebras Associated to Automorphisms of Elliptic Curves. In The Grothendieck Festschrift, pages 33–85. Springer, 1990.M. Artin, J. Tate, and M. Van den Bergh. Modules over regular algebras of dimension 3. Invent. Math., 106(2):335–388, 1991V. V. Bavula. Description of bi-quadratic algebras on 3 generators with PBW basis. J. Algebra, 631:695–730, 2023.L. Bokut and Y. Chen. Gröbner-Shirshov bases and their calculation. Bull. Math. Sci., 4(3):325–395, 2014.L. Bokut and Y. Chen. Gröbner-Shirshov bases theory and Shirshov algorithm. Novosibirsk: RIZ NSU, 2014.Y. Bai and Y. Chen. Gröbner-Shirshov bases theory for Leibniz superalgebras. Comm. Algebra, 50(8):3524–3542, 2022Y. Bai, Y. Chen, and Z. Zhang. Gelfand-Kirillov dimension of bicommutative algebras. Linear Multilinear Algebra, 70(22):7623–7649, 2021G. M. Bergman. The Diamond lemma for ring theory. Adv. Math., 29(2):178–218, 1978L. Bokut, Y. Fong, and W.F. Ke. Gröbner-Shirshov bases and composition lemma for associative conformal algebras: an example. Contemp. Math., 264:63–90, 2000.A. Bell and K. Goodearl. Uniform rank over differential operator rings and Poincaré-Birkhoff-Witt extensions. Pacific J. Math., 131(1):13–37, 1988J. Bueso, J. Gómez-Torrecillas, and A. Verschoren. Algorithmic Methods in Non-Commutative Algebra: Applications to Quantum Groups. Mathematical Modelling: Theory and Applications, Springer, 2003.L. Bokut and P. Malcolmson. Gröbner-Shirshov bases for quantum enveloping algebras. Israel J. Math., 96:97–113, 1996L. Bokut and L. Makar-Limanov. A basis of a free metabelian associative algebra. Sib. Math. J., 32(6):910–915, 1991L. Bokut. Unsolvability of the equality problem and subalgebras of finitely presented Lie algebras. Izv. Ross. Akad. Nauk Ser. Mat., 36(6):1173–1219, 1972.L. Bokut. Embeddings into simple associative algebras. Algebra Logika, 15(2):117–142, 1976G. Bellamy, D. Rogalski, T. Schedler, J. Stafford, and M. Wemyss. Noncom- mutative Algebraic Geometry, volume 64. Cambridge University Press, 2016.A. D. Bell and S. P. Smith. Some 3-dimensional skew polynomial rings. University of Wisconsin, Milwaukee, preprint, 1990.B. Buchberger. An algorithm for finding a basis for the residue class ring of a zero-dimensional polynomial ideal (PhD thesis in German). Institute University of Innsbruck, 1965B. Buchberger. An algorithmical criteria for the solvability of algebraic systems of equations. Aequationes Math, 4:374–383, 1970I. V. Cherednik. On R-matrix quantization of formal loop groups. Group theoretical methods in physics, 2:161–180, 1986.A. Chirvasitu and S. P. Smith. Some algebras having relations like those for the 4-dimensional Sklyanin algebras. J. Korean Math. Soc., 60(4):745–777, 2023.T. Cassidy and M. Vancliff. Generalizations of Graded Clifford Algebras and of Complete Intersections. J. Lond. Math. Soc., 81(1):91–112, 2010.V. G. Drinfeld. Quantum Groups. Zapiski Nauchnykh Seminarov POMI, 155:18– 49, 1986.W. Fajardo, C. Gallego, O. Lezama, A. Reyes, H. Suárez, and H. Venegas. Skew PBW Extensions. Ring and Module-theoretic Properties, Matrix and Gröbner Methods, and Applications. Springer, Cham, 2020.B. L. Feigin and A. V. Odesskii. Sklyanin algebras associated with an elliptic curve. Preprint deposited with Institute of Theoretical Physics of the Academy of Sciences of the Ukrainian SSR, page 33, 1989.B. L. Feigin and A. V. Odesskii. Sklyanin elliptic algebras. Funct. Anal. Appl., 23(3):207–214, 1989A. V. Golovashkin and V. M. Maksimov. Skew Ore polynomials of higher orders generated by homogeneous quadratic relations. Russian Math. Surveys, 53(2):384–386, 1998.E. L. Green. Noncommutative Gröbner bases, and projective resolutions. In Computational Methods for Representations of Groups and Algebras: Euroconference in Essen (Germany), April 1–5, 1977, pages 29–60. Springer, 1999.P. P. Grivel. Une histoire du théorème de Poincare-Birkhoff-Witt. Expo. Math., 22(2):145–184, 2004.K. R. Goodearl and R. B. Warfield. An Introduction to Noncommutative Noetherian Rings. Cambridge University Press. London, 2004.J. Huang and Y. Chen. Gröbner- Shirshov Bases Theory for Trialgebras. 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Phys., 10:63–69, 1985.Base de Gröbner-ShirshovAlgoritmo de ShirshovLema del diamanteÁlgebra PBWÁlgebra de SklyaninGröbner-Shirshov basisShirshov's algorithmDiamond lemmaPBW algebraSklyanin algebraLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/86074/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1053587838.2024.pdf1053587838.2024.pdfTesis de Maestría en Ciencia - Matemáticasapplication/pdf1511125https://repositorio.unal.edu.co/bitstream/unal/86074/2/1053587838.2024.pdf04d346b14c21bf525004ae8d26a40e30MD52THUMBNAIL1053587838.2024.pdf.jpg1053587838.2024.pdf.jpgGenerated Thumbnailimage/jpeg4027https://repositorio.unal.edu.co/bitstream/unal/86074/3/1053587838.2024.pdf.jpg561578902a5f067d45d50bd62b29d4b6MD53unal/86074oai:repositorio.unal.edu.co:unal/860742024-08-24 23:14:07.742Repositorio Institucional Universidad Nacional de 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Gröbner-Shirshov bases for Sklyanin algebras

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