Uma construção alternativa para o funtor de Happel

Detalhes bibliográficos
Autor(a) principal: Lima, Maria Elismara de Sousa
Data de Publicação: 2018
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFS
Texto Completo: http://ri.ufs.br/jspui/handle/riufs/7782
Resumo: The aim of this dissertation is to present a simpli cation of the proof of the following result obtained rst by Happel in [3]: If A is a nite-dimensional algebra over a eld algebraically closed K, then there is a triangulated, full and faithful functor of triangulated categories H : Db(modA) ! modA^, where A^ is the repetitive algebra obtained from A, which is also dense if A is of nite global dimension. We begin with a succinct presentation of the categorical language, approaching in general terms on the localization of categories, triangulated categories and their localizations, and nally derived categories, which are localized and triangulated categories. We also introduce the stable category of modules of a repetitive algebra A^. In the last chapter, we demonstrate the main result with the help of a result found in [8], in addition to the previously mentioned concepts.
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spelling Lima, Maria Elismara de SousaSilva, Danilo Dias da2018-04-17T19:28:00Z2018-04-17T19:28:00Z2018-02-23LIMA, Maria Elismara de Sousa. Uma construção alternativa para o funtor de Happel. 2018. 113 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Sergipe, São Cristovão, SE, 2018.http://ri.ufs.br/jspui/handle/riufs/7782The aim of this dissertation is to present a simpli cation of the proof of the following result obtained rst by Happel in [3]: If A is a nite-dimensional algebra over a eld algebraically closed K, then there is a triangulated, full and faithful functor of triangulated categories H : Db(modA) ! modA^, where A^ is the repetitive algebra obtained from A, which is also dense if A is of nite global dimension. We begin with a succinct presentation of the categorical language, approaching in general terms on the localization of categories, triangulated categories and their localizations, and nally derived categories, which are localized and triangulated categories. We also introduce the stable category of modules of a repetitive algebra A^. In the last chapter, we demonstrate the main result with the help of a result found in [8], in addition to the previously mentioned concepts.O objetivo dessa disserta c~ao e trazer uma simpli ca c~ao da demonstra c~ao do seguinte resultado obtido primeiramente por Happel [3]: Se A e uma K- algebra de dimens~ao nita, ent~ao existe um funtor pleno, el e triangulado H : Db(modA) ! modA^, onde A^ e a a lgebra repetitiva obtida de A, que e tamb em denso se A e de dimensa~o global nita. Iniciamos com uma apresenta c~ao sucinta da linguagem categ orica, abordando de maneira geral sobre localiza c~ao de categorias, categorias trianguladas e suas localiza c~oes, e nalmente categorias derivadas, que s~ao categorias localizadas e trianguladas. Tamb em introduzimos a categoria est avel de m odulos da algebra repetitiva de A. No ultimo cap tulo, demonstramos o resultado principal com o aux lio de um resultado encontrado em [8], al em dos conceitos citados anteriormente.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESSão Cristóvão, SEporMatemáticaÁlgebraÁlgebra homológicaCategorias (Matemática)Localização de categoriasCategorias trianguladasCategoria derivadaLocalization of categoriesTriangulated categoriesDerived categoryUma construção alternativa para o funtor de Happelinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisPós-Graduação em MatemáticaUniversidade Federal de Sergipereponame:Repositório Institucional da UFSinstname:Universidade Federal de Sergipe (UFS)instacron:UFSinfo:eu-repo/semantics/openAccessLICENSElicense.txtlicense.txttext/plain; charset=utf-81475https://ri.ufs.br/jspui/bitstream/riufs/7782/1/license.txt098cbbf65c2c15e1fb2e49c5d306a44cMD51ORIGINALMARIA_ELISMARA_SOUSA_LIMA.pdfMARIA_ELISMARA_SOUSA_LIMA.pdfapplication/pdf1026395https://ri.ufs.br/jspui/bitstream/riufs/7782/2/MARIA_ELISMARA_SOUSA_LIMA.pdf8868b7e4631d377e6827a1781c4a01b7MD52TEXTMARIA_ELISMARA_SOUSA_LIMA.pdf.txtMARIA_ELISMARA_SOUSA_LIMA.pdf.txtExtracted texttext/plain139535https://ri.ufs.br/jspui/bitstream/riufs/7782/3/MARIA_ELISMARA_SOUSA_LIMA.pdf.txtdee8e85d01231bb6a53427684f02fdaaMD53THUMBNAILMARIA_ELISMARA_SOUSA_LIMA.pdf.jpgMARIA_ELISMARA_SOUSA_LIMA.pdf.jpgGenerated Thumbnailimage/jpeg1391https://ri.ufs.br/jspui/bitstream/riufs/7782/4/MARIA_ELISMARA_SOUSA_LIMA.pdf.jpgb1568c92ab4ab33add84f51c6dca935bMD54riufs/77822018-04-17 16:28:00.802oai:ufs.br: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Repositório InstitucionalPUBhttps://ri.ufs.br/oai/requestrepositorio@academico.ufs.bropendoar:2018-04-17T19:28Repositório Institucional da UFS - Universidade Federal de Sergipe (UFS)false
dc.title.pt_BR.fl_str_mv Uma construção alternativa para o funtor de Happel
title Uma construção alternativa para o funtor de Happel
spellingShingle Uma construção alternativa para o funtor de Happel
Lima, Maria Elismara de Sousa
Matemática
Álgebra
Álgebra homológica
Categorias (Matemática)
Localização de categorias
Categorias trianguladas
Categoria derivada
Localization of categories
Triangulated categories
Derived category
title_short Uma construção alternativa para o funtor de Happel
title_full Uma construção alternativa para o funtor de Happel
title_fullStr Uma construção alternativa para o funtor de Happel
title_full_unstemmed Uma construção alternativa para o funtor de Happel
title_sort Uma construção alternativa para o funtor de Happel
author Lima, Maria Elismara de Sousa
author_facet Lima, Maria Elismara de Sousa
author_role author
dc.contributor.author.fl_str_mv Lima, Maria Elismara de Sousa
dc.contributor.advisor1.fl_str_mv Silva, Danilo Dias da
contributor_str_mv Silva, Danilo Dias da
dc.subject.por.fl_str_mv Matemática
Álgebra
Álgebra homológica
Categorias (Matemática)
Localização de categorias
Categorias trianguladas
Categoria derivada
topic Matemática
Álgebra
Álgebra homológica
Categorias (Matemática)
Localização de categorias
Categorias trianguladas
Categoria derivada
Localization of categories
Triangulated categories
Derived category
dc.subject.eng.fl_str_mv Localization of categories
Triangulated categories
Derived category
description The aim of this dissertation is to present a simpli cation of the proof of the following result obtained rst by Happel in [3]: If A is a nite-dimensional algebra over a eld algebraically closed K, then there is a triangulated, full and faithful functor of triangulated categories H : Db(modA) ! modA^, where A^ is the repetitive algebra obtained from A, which is also dense if A is of nite global dimension. We begin with a succinct presentation of the categorical language, approaching in general terms on the localization of categories, triangulated categories and their localizations, and nally derived categories, which are localized and triangulated categories. We also introduce the stable category of modules of a repetitive algebra A^. In the last chapter, we demonstrate the main result with the help of a result found in [8], in addition to the previously mentioned concepts.
publishDate 2018
dc.date.accessioned.fl_str_mv 2018-04-17T19:28:00Z
dc.date.available.fl_str_mv 2018-04-17T19:28:00Z
dc.date.issued.fl_str_mv 2018-02-23
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv LIMA, Maria Elismara de Sousa. Uma construção alternativa para o funtor de Happel. 2018. 113 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Sergipe, São Cristovão, SE, 2018.
dc.identifier.uri.fl_str_mv http://ri.ufs.br/jspui/handle/riufs/7782
identifier_str_mv LIMA, Maria Elismara de Sousa. Uma construção alternativa para o funtor de Happel. 2018. 113 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Sergipe, São Cristovão, SE, 2018.
url http://ri.ufs.br/jspui/handle/riufs/7782
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.program.fl_str_mv Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv Universidade Federal de Sergipe
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