Algorithms of differentiation for posets with an involution
ilustraciones, graficas
- Autores:
-
Cifuentes Vargas, Verónica
- Tipo de recurso:
- Doctoral thesis
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/81993
- Palabra clave:
- 510 - Matemáticas::512 - Álgebra
Teoría de representación de conjuntos parcialmente ordenados
Teoría de Auslander-Reiten
algoritmos de diferenciación
Problema matricial
Representación vectorial
Representation Theory of Partially Ordered Sets
Auslander-Reiten theory
Differentiation algorithms
Vector Space Representation
Differentiation algorithms
- Rights
- openAccess
- License
- Atribución-SinDerivadas 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Algorithms of differentiation for posets with an involution |
| dc.title.translated.spa.fl_str_mv |
Algoritmos de diferención para posets con involución |
| title |
Algorithms of differentiation for posets with an involution |
| spellingShingle |
Algorithms of differentiation for posets with an involution 510 - Matemáticas::512 - Álgebra Teoría de representación de conjuntos parcialmente ordenados Teoría de Auslander-Reiten algoritmos de diferenciación Problema matricial Representación vectorial Representation Theory of Partially Ordered Sets Auslander-Reiten theory Differentiation algorithms Vector Space Representation Differentiation algorithms |
| title_short |
Algorithms of differentiation for posets with an involution |
| title_full |
Algorithms of differentiation for posets with an involution |
| title_fullStr |
Algorithms of differentiation for posets with an involution |
| title_full_unstemmed |
Algorithms of differentiation for posets with an involution |
| title_sort |
Algorithms of differentiation for posets with an involution |
| dc.creator.fl_str_mv |
Cifuentes Vargas, Verónica |
| dc.contributor.advisor.none.fl_str_mv |
Bautista Ramos, Raymundo Moreno Cañadas, Agustín |
| dc.contributor.author.none.fl_str_mv |
Cifuentes Vargas, Verónica |
| dc.contributor.researchgroup.spa.fl_str_mv |
Terenufia-Unal |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas::512 - Álgebra |
| topic |
510 - Matemáticas::512 - Álgebra Teoría de representación de conjuntos parcialmente ordenados Teoría de Auslander-Reiten algoritmos de diferenciación Problema matricial Representación vectorial Representation Theory of Partially Ordered Sets Auslander-Reiten theory Differentiation algorithms Vector Space Representation Differentiation algorithms |
| dc.subject.proposal.spa.fl_str_mv |
Teoría de representación de conjuntos parcialmente ordenados Teoría de Auslander-Reiten algoritmos de diferenciación Problema matricial Representación vectorial |
| dc.subject.proposal.eng.fl_str_mv |
Representation Theory of Partially Ordered Sets Auslander-Reiten theory Differentiation algorithms Vector Space Representation Differentiation algorithms |
| description |
ilustraciones, graficas |
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2021 |
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2021-07 |
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2022-08-22T19:40:40Z |
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2022-08-22T19:40:40Z |
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Trabajo de grado - Doctorado |
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Repositorio Institucional Universidad Nacional de Colombia |
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eng |
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eng |
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RedCol LaReferencia |
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D.M. Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets. CMS Books in Mathematics. Volume 2. Springer. 2000. 244 I. Assem; D. Simson; A. Skowronski. Elements of the Representation Theory of Associative Algebras. Cambridge University Press. 2006. M. Auslander, S. O. Smalo. Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics. Volume 36. Cambridge Univeristy Press. 1995. M. Auslander, I. Reiten. Representation theory of Artin algebras III. Communications in Algebra. Cambridge Univeristy Press. Volume 3. 1975. R. Bautista, R. Martinez-Villa. Representation of Partially Ordered Set and 1-Gorenstein Artin Algebras. Proceedings, Conference on Ring Theory, Antwerp.Lect. Notes. Pure Appl. Math. Volume 51. 1979. R. Bautista. On algebras of strongly unbounded type. Comm. Math. Helv. Volume 60. 1985. R. Bautista, I. Dorado. Algebraically equipped poset. Boletín de la Sociedad Matemática Mexicana. Volume 23. 2017. V.M. Bondarenko, A.G. Zavadskij. Posets with an equivalence relation of tame type and of finite growth. Can. Math. Soc. conf. Proc. Volume 11. 1991. V.M. Bondarenko, L.A. Nazarova, A.V. Roiter. Tame partially ordered sets with involution. Proc. Steklov Inst. Math. Volume 183. 1991. K. Bongartz. Indecomposables are standard. Comment. Math. Helvetici. Volume 60. 1985. A.M. Cañadas, A.G. Zavadskij. Categorical description of some differentiation algorithms. Journal of Algebra and Its Applications. Volume 5. 2006. Number 5. A.M. Cañadas, Categorical properties of the algorithm of differentiation VII for equipped posets. JPANTA. Volume 25. 2012. A.M. Cañadas, I.D.M. Gaviria, P.F.F. Espinosa. On the algorithm of differentiation D-IX for equipped posets. JPANTA. Volume 29. 2013. Number 12. A.M. Cañadas, I.D.M. Gaviria, J.S. Mora. On the Gabriel's quiver of some equipped posets. JPANTA. Volume 36. 2015. Number 1. Y.A. Drozd. Matrix Problems and Categories of matrices. Zap. Nauchn. Sem. Leningrad. Otel. Math. Inst. Stelov. LOMI. Volume 28. 1972. P. Gabriel, Representations indecomposables des ensembles ordonnes. Semin. P. Dubreil, 26 annee 1972/73, Algebre, Expose. Volume 13. 1973. P. Gabriel, A.V. Roiter. Representations of Finite Dimensional Algebras. Algebra VIII, Encyclopedia of Math.Sc. Springer-Verlag. Volume 73. 1992 M.M. Kleiner. Partially ordered sets of finite type. Zap. Nauchn. Semin. LOMI. Volume 28. 1972. Translation: J. Sov. Math. Volume 3. Number 5. 1975. S. Liu. Auslander-Reiten theory in a Krull-Schmidt category. Sao Paulo Journal of Mathematical Sciences. 2010. A.V. Roiter, L.A. Nazarova. Representations of partially ordered sets. Zap. Nauchn. Semin. LOMI. Kiev. (in Russian). 1972. Volume 28. Translation: {J. Sov. Math. Volume 3. 1975. L.A. Nazarova, A.V. Roiter. Categorical matrix problems and the Brauer-Thrall conjecture. Preprint Inst. Math.AN UkSSR, Ser. Mat. Volume 73. 1973. (in Russian). Translation: Mitt.Math. Semin. Giessen. Volume 115. 1975. L.A. Nazarova, A.V. Roiter. Partially ordered sets of infinite type. Izv. AN SSSR, Ser. Mat.. Volume 39. Number 5. 1975. in Russian. Translation: Math. USSR Izvestia. Volume 9. 1975. L.A. Nazarova, A.V. Roiter. Representations and forms of weakly completed partially ordered sets. Linear algebra and representation theory. Akad. Nauk Ukrain. SSR Inst. Mat., Kiev. 1977. L.A. Nazarova, A.V. Roiter. Representations of bipartite completed posets. Comment. Math. Helv. Volume 63. 1988. L.A. Nazarova, A.G. Zavadskij. Partially ordered sets of tame type. Matrix problems. Akad. Nauk Ukrain. SSR Inst. Mat., Kiev. 1977. L.A. Nazarova, {A.G. Zavadskij. Partially ordered sets of finite growth. Function. Anal. i Prilozhen. AMS. Volume 19. 1982. Number 2. (in Russian). Translation: Functional. Anal. Appl. Volume 16. 1982. C.M. Ringel. Tame Algebras and Integral Quadratic Forms. Volume 1099. Springer-Verlag.1984. A.V. Roiter. Unboundedness of dimensions of indecomposable representations of algebras having infinitely many indecomposable representations. Izv. Akad. Nauk SSSR Ser. Mat. Volume 32. 1968. (in Russian). Translation:{Math.USSR Izvestia. Volume 2. 1968. D. Simson. Linear Representations of Partially Ordered Sets and Vector Space Categories. Gordon and Breach, London. 1992. K. Spindler. Abstract Algebra with Applications. Volume I. Marcel Dekker, Inc, New York, Basel, Hong kong. 1994. A.V. Zabarilo, A.G. Zavadskij. One-parameter equipped posets and their representations. Functional. Anal.i Prilozhen. Volume 34. Number 2. 2000. (Russian). Translation: Functional Anal. Appl. Volume 34. Number 2. 2.000 A.G. Zavadskij. Differentiation with respect to a pair of points. Matrix problems, Collect. sci. Works. Kiev. Collect. sci. Works. Kiev. 1977 (in Russian). A.G. Zavadskij. The Auslander-Reiten quiver for posets of finite growth. Topics in Algebra, Banach Center Publ. Collect. sci. Works. Kiev. Volume 26. 1990. A.G. Zavadskij. Tame equipped posets. Linear Algebra Appl. AMS. Volume 365. 2003. A.G. Zavadskij. Equipped posets of finite growth. Representations of Algebras and Related Topics, AMS, Fields Inst. Comm. Ser. AMS. Volume 4. 2005. A.G. Zavadskij. On two point differentiation and its generalization. Algebraic Structures and their Representations, AMS, Contemporary Math. Ser. AMS. Volume 376.2005. A.G. Zavadskij, V.V. Kirivcenko. Torsion-free modules over primary rings. Journal of Soviet Mathematics. Volume 11. Number 4. 1979. A.G. Zavadskij. An algorithm for Poset with an Equivalence Relation. Canadian Mathematical Society. Conference Proceedings. Volume 11. 1991. |
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Departamento de Matemáticas |
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Facultad de Ciencias |
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Atribución-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Bautista Ramos, Raymundo9d2752335fa7d32803b3743f4527578fMoreno Cañadas, Agustín9ca55eaf75ecd87559010093e719d1f8Cifuentes Vargas, Verónica1b6a6e56ca83736e536d61ae20d9effcTerenufia-Unal2022-08-22T19:40:40Z2022-08-22T19:40:40Z2021-07https://repositorio.unal.edu.co/handle/unal/81993Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, graficasEn las últimas décadas, el estudio y clasificación de álgebras de dimensión finita con respecto a su tipo de representación ha sido uno de los principales objetivos en la teoría de representaciones de álgebras. Nazarova, Roiter, Zavadskij y Bondarenko introdujeron y estudiaron distintas clases de representaciones asociadas a conjuntos parcialmente ordenados (posets). Aquí estamos interesados, de una parte, en la categoría de representaciones de conjuntos parcialmente ordenados con una relación de equivalencia, donde el conjunto de clases de equivalencia tienen a lo más dos elementos; esta clase de posets se denominan poset con involución. Damos una estructura natural exacta para la categoría de representaciones de esta clase de posets, describimos los objetos proyectivos e inyectivos y probamos la existencia de sucesiones que casi se dividen.Por otro parte, estudiamos las propiedades categóricas de los lagoritmos de diferenciación DI y DIII introducidos por Zavadskij en 1991. (Texto tomado de la fuente)In the last decades, the study and classification of finite-dimensional algebras with respect to their representation type has been one of the main aims in the theory of representations of algebras. Nazarova, Roiter, Zavadskij and Bondarenko have introduced and studied several classes of representations associated to partially ordered sets (posets). Here we are interested, on the one hand, in the category of representations of a poset with an equivalence relation, where the equivalence sets have at most two elements; these kind of posets are called posets with an involution. We give a natural exact structure for the category of representations of this kind of posets, describe the projective, injective objects and prove the existence of almost split sequences. On the other hand, we study the categorical properties of the differentiation algorithms DI and DIII introduced by Zavadskij in 1991DoctoradoDoctor en Ciencias - MatemáticasRepresentation theory of algebrasviii, 96 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Doctorado en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::512 - ÁlgebraTeoría de representación de conjuntos parcialmente ordenadosTeoría de Auslander-Reitenalgoritmos de diferenciaciónProblema matricialRepresentación vectorialRepresentation Theory of Partially Ordered SetsAuslander-Reiten theoryDifferentiation algorithmsVector Space RepresentationDifferentiation algorithmsAlgorithms of differentiation for posets with an involutionAlgoritmos de diferención para posets con involuciónTrabajo de grado - Doctoradoinfo:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/acceptedVersionhttp://purl.org/coar/resource_type/c_db06Texthttp://purl.org/redcol/resource_type/TDRedColLaReferenciaD.M. Arnold, Abelian Groups and Representations of Finite Partially Ordered Sets. CMS Books in Mathematics. Volume 2. Springer. 2000. 244I. Assem; D. Simson; A. Skowronski. Elements of the Representation Theory of Associative Algebras. Cambridge University Press. 2006.M. Auslander, S. O. Smalo. Representation Theory of Artin Algebras. Cambridge Studies in Advanced Mathematics. Volume 36. Cambridge Univeristy Press. 1995.M. Auslander, I. Reiten. Representation theory of Artin algebras III. Communications in Algebra. Cambridge Univeristy Press. Volume 3. 1975.R. Bautista, R. Martinez-Villa. Representation of Partially Ordered Set and 1-Gorenstein Artin Algebras. Proceedings, Conference on Ring Theory, Antwerp.Lect. Notes. Pure Appl. Math. Volume 51. 1979.R. Bautista. On algebras of strongly unbounded type. Comm. Math. Helv. Volume 60. 1985.R. Bautista, I. Dorado. Algebraically equipped poset. Boletín de la Sociedad Matemática Mexicana. Volume 23. 2017.V.M. Bondarenko, A.G. Zavadskij. Posets with an equivalence relation of tame type and of finite growth. Can. Math. Soc. conf. Proc. Volume 11. 1991.V.M. Bondarenko, L.A. Nazarova, A.V. Roiter. Tame partially ordered sets with involution. Proc. Steklov Inst. Math. Volume 183. 1991.K. Bongartz. Indecomposables are standard. Comment. Math. Helvetici. Volume 60. 1985.A.M. Cañadas, A.G. Zavadskij. Categorical description of some differentiation algorithms. Journal of Algebra and Its Applications. Volume 5. 2006. Number 5.A.M. Cañadas, Categorical properties of the algorithm of differentiation VII for equipped posets. JPANTA. Volume 25. 2012.A.M. Cañadas, I.D.M. Gaviria, P.F.F. Espinosa. On the algorithm of differentiation D-IX for equipped posets. JPANTA. Volume 29. 2013. Number 12.A.M. Cañadas, I.D.M. Gaviria, J.S. Mora. On the Gabriel's quiver of some equipped posets. JPANTA. Volume 36. 2015. Number 1.Y.A. Drozd. Matrix Problems and Categories of matrices. Zap. Nauchn. Sem. Leningrad. Otel. Math. Inst. Stelov. LOMI. Volume 28. 1972.P. Gabriel, Representations indecomposables des ensembles ordonnes. Semin. P. Dubreil, 26 annee 1972/73, Algebre, Expose. Volume 13. 1973.P. Gabriel, A.V. Roiter. Representations of Finite Dimensional Algebras. Algebra VIII, Encyclopedia of Math.Sc. Springer-Verlag. Volume 73. 1992M.M. Kleiner. Partially ordered sets of finite type. Zap. Nauchn. Semin. LOMI. Volume 28. 1972. Translation: J. Sov. Math. Volume 3. Number 5. 1975.S. Liu. Auslander-Reiten theory in a Krull-Schmidt category. Sao Paulo Journal of Mathematical Sciences. 2010.A.V. Roiter, L.A. Nazarova. Representations of partially ordered sets. Zap. Nauchn. Semin. LOMI. Kiev. (in Russian). 1972. Volume 28. Translation: {J. Sov. Math. Volume 3. 1975.L.A. Nazarova, A.V. Roiter. Categorical matrix problems and the Brauer-Thrall conjecture. Preprint Inst. Math.AN UkSSR, Ser. Mat. Volume 73. 1973. (in Russian). Translation: Mitt.Math. Semin. Giessen. Volume 115. 1975.L.A. Nazarova, A.V. Roiter. Partially ordered sets of infinite type. Izv. AN SSSR, Ser. Mat.. Volume 39. Number 5. 1975. in Russian. Translation: Math. USSR Izvestia. Volume 9. 1975.L.A. Nazarova, A.V. Roiter. Representations and forms of weakly completed partially ordered sets. Linear algebra and representation theory. Akad. Nauk Ukrain. SSR Inst. Mat., Kiev. 1977.L.A. Nazarova, A.V. Roiter. Representations of bipartite completed posets. Comment. Math. Helv. Volume 63. 1988.L.A. Nazarova, A.G. Zavadskij. Partially ordered sets of tame type. Matrix problems. Akad. Nauk Ukrain. SSR Inst. Mat., Kiev. 1977.L.A. Nazarova, {A.G. Zavadskij. Partially ordered sets of finite growth. Function. Anal. i Prilozhen. AMS. Volume 19. 1982. Number 2. (in Russian). Translation: Functional. Anal. Appl. Volume 16. 1982.C.M. Ringel. Tame Algebras and Integral Quadratic Forms. Volume 1099. Springer-Verlag.1984.A.V. Roiter. Unboundedness of dimensions of indecomposable representations of algebras having infinitely many indecomposable representations. Izv. Akad. Nauk SSSR Ser. Mat. Volume 32. 1968. (in Russian). Translation:{Math.USSR Izvestia. Volume 2. 1968.D. Simson. Linear Representations of Partially Ordered Sets and Vector Space Categories. Gordon and Breach, London. 1992.K. Spindler. Abstract Algebra with Applications. Volume I. Marcel Dekker, Inc, New York, Basel, Hong kong. 1994.A.V. Zabarilo, A.G. Zavadskij. One-parameter equipped posets and their representations. Functional. Anal.i Prilozhen. Volume 34. Number 2. 2000. (Russian). Translation: Functional Anal. Appl. Volume 34. Number 2. 2.000A.G. Zavadskij. Differentiation with respect to a pair of points. Matrix problems, Collect. sci. Works. Kiev. Collect. sci. Works. Kiev. 1977 (in Russian).A.G. Zavadskij. The Auslander-Reiten quiver for posets of finite growth. Topics in Algebra, Banach Center Publ. Collect. sci. Works. Kiev. Volume 26. 1990.A.G. Zavadskij. Tame equipped posets. Linear Algebra Appl. AMS. Volume 365. 2003.A.G. Zavadskij. Equipped posets of finite growth. Representations of Algebras and Related Topics, AMS, Fields Inst. Comm. Ser. AMS. Volume 4. 2005.A.G. Zavadskij. On two point differentiation and its generalization. Algebraic Structures and their Representations, AMS, Contemporary Math. Ser. AMS. Volume 376.2005.A.G. Zavadskij, V.V. Kirivcenko. Torsion-free modules over primary rings. Journal of Soviet Mathematics. Volume 11. Number 4. 1979.A.G. Zavadskij. An algorithm for Poset with an Equivalence Relation. Canadian Mathematical Society. Conference Proceedings. Volume 11. 1991.InvestigadoresORIGINAL52242740.2021.pdf52242740.2021.pdfTesis de Doctorado en Matemáticasapplication/pdf1252393https://repositorio.unal.edu.co/bitstream/unal/81993/1/52242740.2021.pdf5307289d6996293a964e330838b66130MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/81993/2/license.txt8153f7789df02f0a4c9e079953658ab2MD52THUMBNAIL52242740.2021.pdf.jpg52242740.2021.pdf.jpgGenerated Thumbnailimage/jpeg3835https://repositorio.unal.edu.co/bitstream/unal/81993/3/52242740.2021.pdf.jpgcdaf3a06bbcec78a8366558bf210f678MD53unal/81993oai:repositorio.unal.edu.co:unal/819932023-08-07 23:03:44.038Repositorio Institucional Universidad Nacional de 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