Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones
ilustraciones, gráficas
- Autores:
-
Fúneme Mateus, Cristian Camilo
- Tipo de recurso:
- Fecha de publicación:
- 2021
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/81057
- Palabra clave:
- 510 - Matemáticas::512 - Álgebra
Álgebra
Matemáticas
Teoría de grafos
Algebra
Mathematics
Graph theory
Álgebras de configuración de Brauer
Carcaj
Matriz de mensajes
Región de mutación
Región de congelamiento
Brauer configuration algebras
Quiver
Message matrix
Mutation region
Freezing region
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| dc.title.translated.eng.fl_str_mv |
Biserial algebras, Brauer graph algebras and some of its applications |
| title |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| spellingShingle |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones 510 - Matemáticas::512 - Álgebra Álgebra Matemáticas Teoría de grafos Algebra Mathematics Graph theory Álgebras de configuración de Brauer Carcaj Matriz de mensajes Región de mutación Región de congelamiento Brauer configuration algebras Quiver Message matrix Mutation region Freezing region |
| title_short |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| title_full |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| title_fullStr |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| title_full_unstemmed |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| title_sort |
Álgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicaciones |
| dc.creator.fl_str_mv |
Fúneme Mateus, Cristian Camilo |
| dc.contributor.advisor.spa.fl_str_mv |
Moreno Cañadas, Agustín |
| dc.contributor.author.spa.fl_str_mv |
Fúneme Mateus, Cristian Camilo |
| 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 Álgebra Matemáticas Teoría de grafos Algebra Mathematics Graph theory Álgebras de configuración de Brauer Carcaj Matriz de mensajes Región de mutación Región de congelamiento Brauer configuration algebras Quiver Message matrix Mutation region Freezing region |
| dc.subject.lemb.spa.fl_str_mv |
Álgebra Matemáticas Teoría de grafos |
| dc.subject.lemb.eng.fl_str_mv |
Algebra Mathematics Graph theory |
| dc.subject.proposal.spa.fl_str_mv |
Álgebras de configuración de Brauer Carcaj Matriz de mensajes Región de mutación Región de congelamiento |
| dc.subject.proposal.eng.fl_str_mv |
Brauer configuration algebras Quiver Message matrix Mutation region Freezing region |
| description |
ilustraciones, gráficas |
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2021 |
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2021-11 |
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2022-02-24T21:01:57Z |
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2022-02-24T21:01:57Z |
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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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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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spa |
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T. Aihara, Derived equivalences between symmetric special biserial algebras, https://arxiv.org/pdf/1312.0328.pdf, (2014). M.A. Antipov, Derived equivalence of symmetric special biserial algebras, Journal of Mathematical Sciences 147 (2007), no. 5, 6981-6994. I. Assem, D. Simson, and A. Skowronski, Elements of the representation theory of associative algebras, volume 1, techniques of representation theory, (2006). I. Assem and S. Trepode, Homological methods, representation theory and cluster algebras, (2018). C. Cohecha, Teorema del binomio y aplicaciones, Universidad Nacional de Colombia, Facultad de Ciencias (2014). Mg. Thesis. Bogotá. L. Demonet, Algebras of partial triangulations, arXiv:1602.01592 (2016). P.W. Donovan and M.R Freislich, The indecomposable modular representations of certain groups with dihedral sylow subgroup, Mathematische Annalen 238 (1978), no. 3, 207-216. J.A. Drozd, Tame and wild matrix problems, in: V.O. Dlab, and P. Gabriel (eds.) Representation Theory II, Springer Lecture Notes in Mathematics 832 (1980), 242- 258. G.K. Eagelson, A characterization theorem for positive definite sequences of the krawtchouk polynomials, Australian J. Stat 11, (1969), 29-38. K. Erdmann, Algebras with non-periodic bounded modules, Journal of Algebra 475 (2017), 308-326. P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum random walks, Contemporary Mathematics 287, (2001), 89-36. P. Feinsilver and R. Schott, Krawtchouk polynomials and finite probability theory, Probability Measures on Groups X, Plenum, (1991), 129-135. P. Fernández, Categorification of some integer sequences and its applications, Universidad Nacional de Colombia, Facultad de Ciencias (2021). PhD Thesis. Bogotá. K. Fuller, Biserial rings, in: Ring theory, proc. conf., univ. waterloo, waterloo, Lecture Notes in Math (1978), 64-90. P. Gabriel, Auslander-reiten sequences and representation-finite algebras, Lecture Notes in Mat. 831 (1980), 1-71. P. Gabriel, Indecomposable representations 2, Symposia Mat. Inst. Naz. Alta Mat. 11 (1973), 81-104. P. Gabriel, Unzerlegbare darstellungen 1, Manuscripta Math 6 (1972), 71-103. J. Villa; M. Duque; A. Gauthier and N. Rakoto, Modelamiento y control de sistemas híbridos, Revista de ingeniería 6, (2004), 177-182. I.M. Gelfand and V.A. Ponomarev, Indecomposable representations of the Lorentz group, Russian Mathematical Surveys 23 (1968), no. 2, 1-58. E. Green and S. Schroll, Brauer configuration algebras: A generalization of brauer graph algebras, Bulletin des Sciences Math ematiques, 141 (2017), 539-572. E. Green and S. Schroll, Multiserial and special multiserial algebras and their representations, Advances in Mathematics (2015), 1-24. E. Green, S. Schroll, and N. Snashall, Group actions and coverings of brauer graph algebras, Glasgow Mathematical Journal 56 (2011), no. 2, 439-464. E. Green, S. Schroll, N. Snashall, and R. Taillefer, The ext algebra of a brauer graph algebra, Journal of noncommutative geometry 11 (2011), no. 2, 537-579. G.J. Janusz, Indecomposable modules for finite groups, Annals of Mathematics 89 (1969), no. 2, 209-241. M. Krawtchouk, Sur la distribution des racines des polynomes orthogonaux, Comptes Rendus 196, (1933), 739-741. M. Krawtchouk, Sur une generalisation des polynomes d'hermite, Comptes Rendus 189, (1929), 620-622. S. Ladkani, Mutation classes of certain quivers with potentials as derived equivalence classes, arXiv:1102.4108 (2011). A. Rattew; Y. Sun; P. Minssen and M. Pistoia, The efficient preparation of normal distributions in quantum registers, arXiv:2009.06601, (2021), 1-30. T. Nakayama, Note on uniserial and generalized uniserial rings, Proc. Imp. Acad. Tokyo 16 (1940), 285-289. I. Hernández; C. Mateos; J. Núñez and Á. Tenorio, Algunas aplicaciones de la teoría de lie a la economía y a las finanzas, Revista de métodos cuantitativos para la economía y la empresa 6, (2008), 74-94. M. Osorio and A. Moreno, Brauer configuration algebras for multimedia based cryptography and security applications, Multimedia Tools and Applications, (2021), https://doi.org/10.1007/s11042-020-10239-3. Z. Pogorzaly and A. Skowronski, Selfinjective biserial standard algebras, Journal of algebra 138 (1991), 491-504. C. M. Ringel, Indecomposables live in all smaller lengths, Bull. Lond. Math. Soc. 43 (2011), 655-660. C.M. Ringel, The indecomposable representations of the dihedral 2-groups, Mathematische Annalen 214 (1975), no. 1, 19-34. K.W. Roggenkamp, Biserial algebras and graphs, In: I. Reiten, S.O. Smalo, O. Solberg (eds.) Algebras and Modules II (Geiranger, 1996), Conference proceedings – Canadian Mathematical Society, Mathematische Annalen 24 (1998), 481-496. R. Schiffler, Quiver representations, Canadian Mathematical Society- Department of Mathematics University of Connecticut, CMS Books in Mathematics, Springer International Publishing (2014). S. Schroll, Brauer graph algebras, Springer, Cham, 2018. In: Assem I., Trepode S. (eds), Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, 177-223. Trivial extensions of gentle algebras and brauer graph algebras, Journal of Algebra 444 (2015), 183-200. A. Sierra, The dimension of the center of a brauer configuration algebra, J. Algebra 510, (2018), 289-318. A. Skowronski and J. Waschbüsch, Representation-finite biserial algebras, Journal of pure and applied mathematics 345 (1983), 172-181. G. Szegö, Orthogonal polynomials, Colloquium Publications, Vol. 23, New York, AMS, revised eddition, (1959), 35-37. D. Vere-Jones, Finite bivariate distributions and semi-groups of nonnegative matrices, Q. J. Math. Oxford 22, 2, (1971), 247-270. B. Wald and J. Waschbüsch, Tame biserial algebras, Journal of algebra, 95 (1985), no. 2, 480-500. A. Zavadskij, On the kronecker problem and related problems of linear algebra, Linear Algebra and its Applications 425, (2007), 26-62. |
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viii, 74 páginas |
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Universidad Nacional de Colombia |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Departamento de 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, Agustín9ca55eaf75ecd87559010093e719d1f8Fúneme Mateus, Cristian Camilod839db390f641dbae77b955d0e26da87600Terenufia-Unal2022-02-24T21:01:57Z2022-02-24T21:01:57Z2021-11https://repositorio.unal.edu.co/handle/unal/81057Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, gráficasEl objetivo principal de este trabajo es estudiar las álgebras de configuración de Brauer. Para esto, se inicia por la exposición de aspectos básicos de la Teoría de representación de carcajes, luego se describen las álgebras biseriales y especial biseriales desde ejemplos y propiedades de ellas que las relacionan con el surgimiento de las álgebras de grafo de Brauer, estas últimas se definen y ejemplifican para hacer la posterior presentación de las álgebras de configuración de Brauer y algunas de sus propiedades. A partir de lo anterior, el presente trabajo ofrece como resultado la definición de las Álgebras de configuración de Brauer asociadas a puntos en el plano, estableciendo ecuaciones que permiten calcular la dimensión de estas álgebras y de su centro. Además, se presentan ejemplos relacionados con la construcción de álgebras de configuración de Brauer asociadas a puntos en el plano, regiones de congelamiento y regiones de mutación, determinando propiedades para ellas. Por último, se presentan algunas conclusiones y recomendaciones que servirán de base para futuros trabajos de investigación. (Texto tomado de la fuente).The main objective of this work is to study Brauer configuration algebras. For this, it begins with the exposition of basic aspects of the representation theory of characters, then biserial and special biserial algebras are described from examples and properties of them that relate them to the emergence of Brauer graph algebras, the latter are defined and exemplified to make the subsequent presentation of Brauer configuration algebras and some of its properties. From the above, the present work offers, as a result, the definition of Brauer configuration algebras associated to points in the plane, establishing equations that allow calculating the dimension of these algebras and their center. In addition, examples related to the construction of Brauer configuration algebras associated to points in the plane, freezing regions, and mutation regions are presented, determining properties for them. Finally, some conclusions and recommendations are presented, which will serve as a basis for future research work.MaestríaMagíster en Ciencias - MatemáticasÁlgebra y combinatoriaviii, 74 páginasapplication/pdfspaUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - Matemáticas::512 - ÁlgebraÁlgebraMatemáticasTeoría de grafosAlgebraMathematicsGraph theoryÁlgebras de configuración de BrauerCarcajMatriz de mensajesRegión de mutaciónRegión de congelamientoBrauer configuration algebrasQuiverMessage matrixMutation regionFreezing regionÁlgebras biseriales, álgebras de grafos de Brauer y algunas de sus aplicacionesBiserial algebras, Brauer graph algebras and some of its applicationsTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMT. Aihara, Derived equivalences between symmetric special biserial algebras, https://arxiv.org/pdf/1312.0328.pdf, (2014).M.A. Antipov, Derived equivalence of symmetric special biserial algebras, Journal of Mathematical Sciences 147 (2007), no. 5, 6981-6994.I. Assem, D. Simson, and A. Skowronski, Elements of the representation theory of associative algebras, volume 1, techniques of representation theory, (2006).I. Assem and S. Trepode, Homological methods, representation theory and cluster algebras, (2018).C. Cohecha, Teorema del binomio y aplicaciones, Universidad Nacional de Colombia, Facultad de Ciencias (2014). Mg. Thesis. Bogotá.L. Demonet, Algebras of partial triangulations, arXiv:1602.01592 (2016).P.W. Donovan and M.R Freislich, The indecomposable modular representations of certain groups with dihedral sylow subgroup, Mathematische Annalen 238 (1978), no. 3, 207-216.J.A. Drozd, Tame and wild matrix problems, in: V.O. Dlab, and P. Gabriel (eds.) Representation Theory II, Springer Lecture Notes in Mathematics 832 (1980), 242- 258.G.K. Eagelson, A characterization theorem for positive definite sequences of the krawtchouk polynomials, Australian J. Stat 11, (1969), 29-38.K. Erdmann, Algebras with non-periodic bounded modules, Journal of Algebra 475 (2017), 308-326.P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum random walks, Contemporary Mathematics 287, (2001), 89-36.P. Feinsilver and R. Schott, Krawtchouk polynomials and finite probability theory, Probability Measures on Groups X, Plenum, (1991), 129-135.P. Fernández, Categorification of some integer sequences and its applications, Universidad Nacional de Colombia, Facultad de Ciencias (2021). PhD Thesis. Bogotá.K. Fuller, Biserial rings, in: Ring theory, proc. conf., univ. waterloo, waterloo, Lecture Notes in Math (1978), 64-90.P. Gabriel, Auslander-reiten sequences and representation-finite algebras, Lecture Notes in Mat. 831 (1980), 1-71.P. Gabriel, Indecomposable representations 2, Symposia Mat. Inst. Naz. Alta Mat. 11 (1973), 81-104.P. Gabriel, Unzerlegbare darstellungen 1, Manuscripta Math 6 (1972), 71-103.J. Villa; M. Duque; A. Gauthier and N. Rakoto, Modelamiento y control de sistemas híbridos, Revista de ingeniería 6, (2004), 177-182.I.M. Gelfand and V.A. Ponomarev, Indecomposable representations of the Lorentz group, Russian Mathematical Surveys 23 (1968), no. 2, 1-58.E. Green and S. Schroll, Brauer configuration algebras: A generalization of brauer graph algebras, Bulletin des Sciences Math ematiques, 141 (2017), 539-572.E. Green and S. Schroll, Multiserial and special multiserial algebras and their representations, Advances in Mathematics (2015), 1-24.E. Green, S. Schroll, and N. Snashall, Group actions and coverings of brauer graph algebras, Glasgow Mathematical Journal 56 (2011), no. 2, 439-464.E. Green, S. Schroll, N. Snashall, and R. Taillefer, The ext algebra of a brauer graph algebra, Journal of noncommutative geometry 11 (2011), no. 2, 537-579.G.J. Janusz, Indecomposable modules for finite groups, Annals of Mathematics 89 (1969), no. 2, 209-241.M. Krawtchouk, Sur la distribution des racines des polynomes orthogonaux, Comptes Rendus 196, (1933), 739-741.M. Krawtchouk, Sur une generalisation des polynomes d'hermite, Comptes Rendus 189, (1929), 620-622.S. Ladkani, Mutation classes of certain quivers with potentials as derived equivalence classes, arXiv:1102.4108 (2011).A. Rattew; Y. Sun; P. Minssen and M. Pistoia, The efficient preparation of normal distributions in quantum registers, arXiv:2009.06601, (2021), 1-30.T. Nakayama, Note on uniserial and generalized uniserial rings, Proc. Imp. Acad. Tokyo 16 (1940), 285-289.I. Hernández; C. Mateos; J. Núñez and Á. Tenorio, Algunas aplicaciones de la teoría de lie a la economía y a las finanzas, Revista de métodos cuantitativos para la economía y la empresa 6, (2008), 74-94.M. Osorio and A. Moreno, Brauer configuration algebras for multimedia based cryptography and security applications, Multimedia Tools and Applications, (2021), https://doi.org/10.1007/s11042-020-10239-3.Z. Pogorzaly and A. Skowronski, Selfinjective biserial standard algebras, Journal of algebra 138 (1991), 491-504.C. M. Ringel, Indecomposables live in all smaller lengths, Bull. Lond. Math. Soc. 43 (2011), 655-660.C.M. Ringel, The indecomposable representations of the dihedral 2-groups, Mathematische Annalen 214 (1975), no. 1, 19-34.K.W. Roggenkamp, Biserial algebras and graphs, In: I. Reiten, S.O. Smalo, O. Solberg (eds.) Algebras and Modules II (Geiranger, 1996), Conference proceedings – Canadian Mathematical Society, Mathematische Annalen 24 (1998), 481-496.R. Schiffler, Quiver representations, Canadian Mathematical Society- Department of Mathematics University of Connecticut, CMS Books in Mathematics, Springer International Publishing (2014).S. Schroll, Brauer graph algebras, Springer, Cham, 2018. In: Assem I., Trepode S. (eds), Homological Methods, Representation Theory, and Cluster Algebras, CRM Short Courses, 177-223.Trivial extensions of gentle algebras and brauer graph algebras, Journal of Algebra 444 (2015), 183-200.A. Sierra, The dimension of the center of a brauer configuration algebra, J. Algebra 510, (2018), 289-318.A. Skowronski and J. Waschbüsch, Representation-finite biserial algebras, Journal of pure and applied mathematics 345 (1983), 172-181.G. Szegö, Orthogonal polynomials, Colloquium Publications, Vol. 23, New York, AMS, revised eddition, (1959), 35-37.D. Vere-Jones, Finite bivariate distributions and semi-groups of nonnegative matrices, Q. J. Math. Oxford 22, 2, (1971), 247-270.B. Wald and J. Waschbüsch, Tame biserial algebras, Journal of algebra, 95 (1985), no. 2, 480-500.A. Zavadskij, On the kronecker problem and related problems of linear algebra, Linear Algebra and its Applications 425, (2007), 26-62.EstudiantesInvestigadoresORIGINAL2949954731.2021.pdf2949954731.2021.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf666185https://repositorio.unal.edu.co/bitstream/unal/81057/3/2949954731.2021.pdf7f6fed93427c3031aaf3797d366bc314MD53LICENSElicense.txtlicense.txttext/plain; charset=utf-84074https://repositorio.unal.edu.co/bitstream/unal/81057/4/license.txt8153f7789df02f0a4c9e079953658ab2MD54THUMBNAIL2949954731.2021.pdf.jpg2949954731.2021.pdf.jpgGenerated Thumbnailimage/jpeg2223https://repositorio.unal.edu.co/bitstream/unal/81057/5/2949954731.2021.pdf.jpg0b547450a4ebc85c8877f6cf5b1c4c45MD55unal/81057oai:repositorio.unal.edu.co:unal/810572023-08-02 23:03:31.082Repositorio Institucional Universidad Nacional de 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