Algunas relaciones entre álgebras de caminos y variedades algebraicas afines
ilustraciones, diagramas, figuras
- Autores:
-
Arteaga Bastidas, Ricardo Hugo
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/85477
- Palabra clave:
- 510 - Matemáticas::512 - Álgebra
510 - Matemáticas::516 - Geometría
Curvas algebraicas
Algebraic varieties
Teorı́a de representación de anillos y álgebras asociativas
Bases de Gröbner no conmutativas
Álgebras de Caminos
Representaciones de carcajes
Variedades algebraicas
Anillos y álgebras asociativas
Representation theory of associative rings and algebras
Non-commutative Gröbner basis
Path algebras
Quiver representations
Algebraic varieties
Associative rings and algebras
Variedades algebraicas
Gröbner bases
Gröbner basis
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| dc.title.translated.eng.fl_str_mv |
Some relationships between path algebras and affine algebraic varieties |
| title |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| spellingShingle |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines 510 - Matemáticas::512 - Álgebra 510 - Matemáticas::516 - Geometría Curvas algebraicas Algebraic varieties Teorı́a de representación de anillos y álgebras asociativas Bases de Gröbner no conmutativas Álgebras de Caminos Representaciones de carcajes Variedades algebraicas Anillos y álgebras asociativas Representation theory of associative rings and algebras Non-commutative Gröbner basis Path algebras Quiver representations Algebraic varieties Associative rings and algebras Variedades algebraicas Gröbner bases Gröbner basis |
| title_short |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| title_full |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| title_fullStr |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| title_full_unstemmed |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| title_sort |
Algunas relaciones entre álgebras de caminos y variedades algebraicas afines |
| dc.creator.fl_str_mv |
Arteaga Bastidas, Ricardo Hugo |
| dc.contributor.advisor.none.fl_str_mv |
Moreno Cañadas, Agustín |
| dc.contributor.author.none.fl_str_mv |
Arteaga Bastidas, Ricardo Hugo |
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Terenufia-Unal |
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510 - Matemáticas::512 - Álgebra 510 - Matemáticas::516 - Geometría |
| topic |
510 - Matemáticas::512 - Álgebra 510 - Matemáticas::516 - Geometría Curvas algebraicas Algebraic varieties Teorı́a de representación de anillos y álgebras asociativas Bases de Gröbner no conmutativas Álgebras de Caminos Representaciones de carcajes Variedades algebraicas Anillos y álgebras asociativas Representation theory of associative rings and algebras Non-commutative Gröbner basis Path algebras Quiver representations Algebraic varieties Associative rings and algebras Variedades algebraicas Gröbner bases Gröbner basis |
| dc.subject.lcc.spa.fl_str_mv |
Curvas algebraicas |
| dc.subject.lcc.eng.fl_str_mv |
Algebraic varieties |
| dc.subject.proposal.spa.fl_str_mv |
Teorı́a de representación de anillos y álgebras asociativas Bases de Gröbner no conmutativas Álgebras de Caminos Representaciones de carcajes Variedades algebraicas Anillos y álgebras asociativas |
| dc.subject.proposal.eng.fl_str_mv |
Representation theory of associative rings and algebras Non-commutative Gröbner basis Path algebras Quiver representations Algebraic varieties Associative rings and algebras |
| dc.subject.wikidata.spa.fl_str_mv |
Variedades algebraicas Gröbner bases |
| dc.subject.wikidata.eng.fl_str_mv |
Gröbner basis |
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ilustraciones, diagramas, figuras |
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2023 |
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2023 |
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2024-01-29T13:27:20Z |
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2024-01-29T13:27:20Z |
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Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/85477 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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spa |
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J. Apel and U. Klaus, Felix, a special computer algebra system for the computation in commutative and non-commutative rings and modules., 1998. http://felix.hgb-leipzig.de/. Ibrahim Assem, Andrzej Skowronski, and Daniel Simson, Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory, Cambridge University Press, 2006. J. Backelin, The grobner basis calculator Bergman, 2006. https://servus.math.su.se/bergman/. Michael Barot, Introduction to the Representation Theory of Algebras, Springer International Pu- blishing, Cham, 2015. https://link.springer.com/10.1007/978-3-319-11475-0. Bruno Buchberger, An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal, Ph.D. Thesis, 1965. Harm Derksen and Jerzy Weyman, An Introduction to Quiver Representations, American Mathematical Society, Providence, Rhode Island, 2017. Y. Drozd, Introduction to Algebraic Geometry, Unpublished Textbook, 2004. P. I. Etingof (ed.), Introduction to representation theory, Student Mathematical Library, American Mathematical Society, Providence, R.I, 2011. D.R. Farkas, C. Feustel, and E.L. Green, Synergy in the theories of Gröbner bases and path algebras, Canad. J. Mathematics 45 (1993), 727– 739. Peter Gabriel, Unzerlegbare Darstellungen I, manuscripta mathematica 6 (March 1972), no. 1, 71– 103. https://doi.org/10.1007/BF01298413. Peter Gabriel, Indecomposable representations. II, 1973. Edward L. Green, Noncommutative Gröbner Bases, and Projective Resolutions, Computational Methods for Representations of Groups and Algebras, 1999, pp. 29– 60. Edward L. Green, Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases, Journal of Symbolic Computation 29 (May 2000), no. 4, 601– 623. http://www.sciencedirect.com/science/article/pii/S0747717199903243. Edward L. Green, Lutz Hille, and Sibylle Schroll, Algebras and Varieties, Algebras and Representation Theory 24 (March 2020), 367– 388. https://doi.org/10.1007/s10468-020-09951-3. William H. Gustafson, The history of algebras and their representations, Representations of Algebras, 1982, pp. 1– 28. Ryan Kinser, Introduction to Geometry of Representation of Algebras. Lecture Notes., 2018. V Levandovsky and G Greuel, Plural. A subsystem for computations with non-commutative polynomial algebras., 2006. https://www.singular.uni-kl.de/. T. Mora, Gröbner bases for non-commutative polynomial rings, Proc. AAECC3, L.N.C.S 229 (1986). Claus Michael Ringel, Report on the Brauer-Thrall conjectures: Rojter’s theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I), Representation Theory I: Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa, Carleton University, August 13 – 18, 1979, 1980, pp. 104– 136. https://doi.org/10.1007/BFb0089780. Claus Michael Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Mathematics, vol. 1099, Springer, Berlin, Heidelberg, 1984. http://link.springer.com/10.1007/BFb0072870. Ralf Schiffler, Quiver Representations, CMS Books in Mathematics, Springer International Publishing, 2014. https://www.springer.com/gp/book/9783319092034. The QPA Team, QPA. Quivers and path algebras., 2011. https://folk.ntnu.no/oyvinso/QPA/. George V Wilson, The Cartan map on categories of graded modules, Journal of Algebra 85 (December 1983), no. 2, 390– 398. https://www.sciencedirect.com/science/article/pii/ 0021869383901035. |
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viii, 115 páginas |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Facultad de Ciencias |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Moreno Cañadas, Agustín9ca55eaf75ecd87559010093e719d1f8Arteaga Bastidas, Ricardo Hugo534f26584fef2b0062b03b6aa6bc4c03Terenufia-Unal2024-01-29T13:27:20Z2024-01-29T13:27:20Z2023https://repositorio.unal.edu.co/handle/unal/85477Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramas, figurasEl objetivo principal de este trabajo es estudiar algunas relaciones entre los cocientes del álgebra de caminos de un carcaj y ciertas variedades algebraicas afines por medio de bases de Gröbner no conmutativas, así como también las propiedades que comparten las álgebras asociadas a una variedad. Con este fin, iniciamos con una exposición de los temas básicos de la teoría de representación de álgebras asociativas, incluyendo una introducción a la geometría de representación de álgebras y su desarrollo con teoría de invariantes geométrica (GIT). Con estos fundamentos, procedemos a revisar la teoría de bases de Gröbner no conmutativas, donde estudiamos los ordenamientos monomiales aplicables a álgebras de caminos y los algoritmos existentes para la obtención de estas bases. Revisamos también los sistemas de software disponibles que automatizan estos cálculos. Posteriormente abordamos conceptos básicos e introductorios de la geometría algebraica. Definimos la topología de Zariski y el célebre teorema de los ceros de Hilbert, temas fundamentales para una comprensión del último capítulo, donde finalmente estudiamos las relaciones entre álgebras de caminos y sus variedades algebraicas asociadas. Allí estudiamos el teorema de correspondencia y cómo las álgebras graduadas se pueden ver como una clase especial de subvariedades. Terminamos esta exposición considerando los ideales admisibles en la construcción de variedades algebraicas afines. Por último, tenemos un capítulo de conclusiones y trabajos futuros, donde revisamos las posibles direcciones de pueden tomar las investigaciones en estas áreas. (Texto tomado de la fuente)The main objective of this work is to study some relationships between the quotients of the path algebra of a quiver and certain affine algebraic varieties using non-commutative Gröbner bases, as well as properties shared by algebras associated with a variety. To this end, we begin with an exposition of the basic themes of the representation theory of associative algebras, including an introduction to the geometry of the representation of algebras and its development with geometric invariant theory (GIT). With these foundations, we review the theory of non-commutative Gröbner bases, where we study the monomial orderings applicable to path algebras and existing algorithms for obtaining these bases. We also review the available software systems that automate these calculations. Later we approach basic and introductory concepts of algebraic geometry. We define the topology of Zariski and Hilbert's famous theorem of zeros, fundamental themes for an understanding of the last chapter, where we finally studied the relationships between path algebras and related algebraic varieties. Over there we study the correspondence theorem and how graded algebras can be seen as a particular class of subvarieties. We end up considering the admissible ideals in constructing related algebraic varieties. Finally, we have a chapter on conclusions and future work, reviewing the possible directions research in these areas can take.MaestríaMagíster en Ciencias - MatemáticasÁlgebraviii, 115 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::512 - Álgebra510 - Matemáticas::516 - GeometríaCurvas algebraicasAlgebraic varietiesTeorı́a de representación de anillos y álgebras asociativasBases de Gröbner no conmutativasÁlgebras de CaminosRepresentaciones de carcajesVariedades algebraicasAnillos y álgebras asociativasRepresentation theory of associative rings and algebrasNon-commutative Gröbner basisPath algebrasQuiver representationsAlgebraic varietiesAssociative rings and algebrasVariedades algebraicasGröbner basesGröbner basisAlgunas relaciones entre álgebras de caminos y variedades algebraicas afinesSome relationships between path algebras and affine algebraic varietiesTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMJ. Apel and U. Klaus, Felix, a special computer algebra system for the computation in commutative and non-commutative rings and modules., 1998. http://felix.hgb-leipzig.de/.Ibrahim Assem, Andrzej Skowronski, and Daniel Simson, Elements of the Representation Theory of Associative Algebras: Volume 1: Techniques of Representation Theory, Cambridge University Press, 2006.J. Backelin, The grobner basis calculator Bergman, 2006. https://servus.math.su.se/bergman/.Michael Barot, Introduction to the Representation Theory of Algebras, Springer International Pu- blishing, Cham, 2015. https://link.springer.com/10.1007/978-3-319-11475-0.Bruno Buchberger, An algorithm for finding a basis for the residue class ring of a zero-dimensional ideal, Ph.D. Thesis, 1965.Harm Derksen and Jerzy Weyman, An Introduction to Quiver Representations, American Mathematical Society, Providence, Rhode Island, 2017.Y. Drozd, Introduction to Algebraic Geometry, Unpublished Textbook, 2004.P. I. Etingof (ed.), Introduction to representation theory, Student Mathematical Library, American Mathematical Society, Providence, R.I, 2011.D.R. Farkas, C. Feustel, and E.L. Green, Synergy in the theories of Gröbner bases and path algebras, Canad. J. Mathematics 45 (1993), 727– 739.Peter Gabriel, Unzerlegbare Darstellungen I, manuscripta mathematica 6 (March 1972), no. 1, 71– 103. https://doi.org/10.1007/BF01298413.Peter Gabriel, Indecomposable representations. II, 1973.Edward L. Green, Noncommutative Gröbner Bases, and Projective Resolutions, Computational Methods for Representations of Groups and Algebras, 1999, pp. 29– 60.Edward L. Green, Multiplicative Bases, Gröbner Bases, and Right Gröbner Bases, Journal of Symbolic Computation 29 (May 2000), no. 4, 601– 623. http://www.sciencedirect.com/science/article/pii/S0747717199903243.Edward L. Green, Lutz Hille, and Sibylle Schroll, Algebras and Varieties, Algebras and Representation Theory 24 (March 2020), 367– 388. https://doi.org/10.1007/s10468-020-09951-3.William H. Gustafson, The history of algebras and their representations, Representations of Algebras, 1982, pp. 1– 28.Ryan Kinser, Introduction to Geometry of Representation of Algebras. Lecture Notes., 2018.V Levandovsky and G Greuel, Plural. A subsystem for computations with non-commutative polynomial algebras., 2006. https://www.singular.uni-kl.de/.T. Mora, Gröbner bases for non-commutative polynomial rings, Proc. AAECC3, L.N.C.S 229 (1986).Claus Michael Ringel, Report on the Brauer-Thrall conjectures: Rojter’s theorem and the theorem of Nazarova and Rojter (on algorithms for solving vectorspace problems. I), Representation Theory I: Proceedings of the Workshop on the Present Trends in Representation Theory, Ottawa, Carleton University, August 13 – 18, 1979, 1980, pp. 104– 136. https://doi.org/10.1007/BFb0089780.Claus Michael Ringel, Tame Algebras and Integral Quadratic Forms, Lecture Notes in Mathematics, vol. 1099, Springer, Berlin, Heidelberg, 1984. http://link.springer.com/10.1007/BFb0072870.Ralf Schiffler, Quiver Representations, CMS Books in Mathematics, Springer International Publishing, 2014. https://www.springer.com/gp/book/9783319092034.The QPA Team, QPA. Quivers and path algebras., 2011. https://folk.ntnu.no/oyvinso/QPA/.George V Wilson, The Cartan map on categories of graded modules, Journal of Algebra 85 (December 1983), no. 2, 390– 398. https://www.sciencedirect.com/science/article/pii/ 0021869383901035.EstudiantesInvestigadoresMaestrosPúblico generalLICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/85477/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL79684796.2023.pdf79684796.2023.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf810574https://repositorio.unal.edu.co/bitstream/unal/85477/2/79684796.2023.pdf9c263bea21b83f40de14ea8229c7ba8bMD52unal/85477oai:repositorio.unal.edu.co:unal/854772024-01-29 09:04:13.179Repositorio Institucional Universidad Nacional de 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