O anel de GREEN da álgebra de TAFT

Detalhes bibliográficos
Ano de defesa: 2019
Autor(a) principal: Pedrotti, Juliana Borges lattes
Orientador(a): Flôres, Daiana Aparecida da Silva lattes
Banca de defesa: Lazzarin, João Roberto lattes, Pogorelsky, Bárbara Seelig lattes
Tipo de documento: Dissertação
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática
Departamento: Matemática
País: Brasil
Palavras-chave em Português:
Álgebra de Taft
Anel de Green
Módulos indecomponíveis
Produto tensorial de módulos
Palavras-chave em Inglês:
Taft algebra
Green ring
Indecomposable modules
Tensor product of modules
Área do conhecimento CNPq:
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.ufsm.br/handle/1/19351
Resumo: The aim of this work is to characterize the Green ring of Taft algebra, denoted by ��(�), where � is a positive integer greater than 1 and � is a primitive root of unity of order �. The Green ring, denoted by �(��(�)), is generated by the isomorphism classes [�] of finite dimensional ��(�)-modules with addition given by [�] + [�] = [� ⊕ �] and multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms of indecomposable finite dimensional ��(�)-modules. In this work we describe the indecomposable ��(�)-modules and the tensorial product between these. From that we show that �(��(�)) is a commutative ring generated by two elements subject to certain relations.
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spelling 2020-01-10T15:30:53Z2020-01-10T15:30:53Z2019-06-28http://repositorio.ufsm.br/handle/1/19351The aim of this work is to characterize the Green ring of Taft algebra, denoted by ��(�), where � is a positive integer greater than 1 and � is a primitive root of unity of order �. The Green ring, denoted by �(��(�)), is generated by the isomorphism classes [�] of finite dimensional ��(�)-modules with addition given by [�] + [�] = [� ⊕ �] and multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms of indecomposable finite dimensional ��(�)-modules. In this work we describe the indecomposable ��(�)-modules and the tensorial product between these. From that we show that �(��(�)) is a commutative ring generated by two elements subject to certain relations.O objetivo deste trabalho é caracterizar o anel de Green da álgebra de Taft, denotada por (), onde é um inteiro positivo maior que 1 e é uma raiz -ésima primitiva da unidade. O anel de Green, denotado por (()), é gerado pelas classes de isomorfismos [] de ()-módulos de dimensão finita com adição dada por [] + [] = [ ⊕ ] e multiplicação dada pelo produto tensorial e possui uma Z-base dada pelas classes de isomorfismos de ()-módulos indecomponíveis de dimensão finita. Neste trabalho descrevemos os ()-módulos indecomponíveis e o produto tensorial entre estes. A partir disto mostramos que (()) é um anel comutativo gerado por dois elementos sujeitos a determinadas relações.porUniversidade Federal de Santa MariaCentro de Ciências Naturais e ExatasPrograma de Pós-Graduação em MatemáticaUFSMBrasilMatemáticaAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessÁlgebra de TaftAnel de GreenMódulos indecomponíveisProduto tensorial de módulosTaft algebraGreen ringIndecomposable modulesTensor product of modulesCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAO anel de GREEN da álgebra de TAFTThe GREEN ring of TAFT algebrainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFlôres, Daiana Aparecida da Silvahttp://lattes.cnpq.br/8009247848619231Della Flora, Saradia Sturzahttp://lattes.cnpq.br/4620247004234154Lazzarin, João Robertohttp://lattes.cnpq.br/6965026304626005Pogorelsky, Bárbara Seelighttp://lattes.cnpq.br/5257746725187169http://lattes.cnpq.br/0326619273813122Pedrotti, Juliana Borges100100000008600522f3c30-9fb4-43e9-a334-f75108196474e2985cc0-3242-48f8-93f4-3e6cba1bb653282f67b4-2f84-4fa8-81d5-68f9795890607f69e1aa-b571-4469-84de-a15366851f3f58082a4b-cd82-4c70-8312-dcd1e21a79a7reponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv O anel de GREEN da álgebra de TAFT
dc.title.alternative.eng.fl_str_mv The GREEN ring of TAFT algebra
title O anel de GREEN da álgebra de TAFT
spellingShingle O anel de GREEN da álgebra de TAFT
Pedrotti, Juliana Borges
Álgebra de Taft
Anel de Green
Módulos indecomponíveis
Produto tensorial de módulos
Taft algebra
Green ring
Indecomposable modules
Tensor product of modules
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short O anel de GREEN da álgebra de TAFT
title_full O anel de GREEN da álgebra de TAFT
title_fullStr O anel de GREEN da álgebra de TAFT
title_full_unstemmed O anel de GREEN da álgebra de TAFT
title_sort O anel de GREEN da álgebra de TAFT
author Pedrotti, Juliana Borges
author_facet Pedrotti, Juliana Borges
author_role author
dc.contributor.advisor1.fl_str_mv Flôres, Daiana Aparecida da Silva
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/8009247848619231
dc.contributor.advisor-co1.fl_str_mv Della Flora, Saradia Sturza
dc.contributor.advisor-co1Lattes.fl_str_mv http://lattes.cnpq.br/4620247004234154
dc.contributor.referee1.fl_str_mv Lazzarin, João Roberto
dc.contributor.referee1Lattes.fl_str_mv http://lattes.cnpq.br/6965026304626005
dc.contributor.referee2.fl_str_mv Pogorelsky, Bárbara Seelig
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/5257746725187169
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/0326619273813122
dc.contributor.author.fl_str_mv Pedrotti, Juliana Borges
contributor_str_mv Flôres, Daiana Aparecida da Silva
Della Flora, Saradia Sturza
Lazzarin, João Roberto
Pogorelsky, Bárbara Seelig
dc.subject.por.fl_str_mv Álgebra de Taft
Anel de Green
Módulos indecomponíveis
Produto tensorial de módulos
topic Álgebra de Taft
Anel de Green
Módulos indecomponíveis
Produto tensorial de módulos
Taft algebra
Green ring
Indecomposable modules
Tensor product of modules
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Taft algebra
Green ring
Indecomposable modules
Tensor product of modules
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description The aim of this work is to characterize the Green ring of Taft algebra, denoted by ��(�), where � is a positive integer greater than 1 and � is a primitive root of unity of order �. The Green ring, denoted by �(��(�)), is generated by the isomorphism classes [�] of finite dimensional ��(�)-modules with addition given by [�] + [�] = [� ⊕ �] and multiplication given by the tensor product and it has a -basis given by the classes of isomorphisms of indecomposable finite dimensional ��(�)-modules. In this work we describe the indecomposable ��(�)-modules and the tensorial product between these. From that we show that �(��(�)) is a commutative ring generated by two elements subject to certain relations.
publishDate 2019
dc.date.issued.fl_str_mv 2019-06-28
dc.date.accessioned.fl_str_mv 2020-01-10T15:30:53Z
dc.date.available.fl_str_mv 2020-01-10T15:30:53Z
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.uri.fl_str_mv http://repositorio.ufsm.br/handle/1/19351
url http://repositorio.ufsm.br/handle/1/19351
dc.language.iso.fl_str_mv por
language por
dc.relation.cnpq.fl_str_mv 100100000008
dc.relation.confidence.fl_str_mv 600
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dc.rights.driver.fl_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática
dc.publisher.initials.fl_str_mv UFSM
dc.publisher.country.fl_str_mv Brasil
dc.publisher.department.fl_str_mv Matemática
publisher.none.fl_str_mv Universidade Federal de Santa Maria
Centro de Ciências Naturais e Exatas
dc.source.none.fl_str_mv reponame:Manancial - Repositório Digital da UFSM
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instname_str Universidade Federal de Santa Maria (UFSM)
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institution UFSM
reponame_str Manancial - Repositório Digital da UFSM
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