Extensões de Hopf-Ore e a décima conjectura de Kaplansky

Detalhes bibliográficos
Ano de defesa: 2019
Autor(a) principal: Garcia, Christian Michel da Cunha lattes
Orientador(a): Flôres, Daiana Aparecida da Silva lattes
Banca de defesa: Morgado, Andrea lattes, Sant'Ana, Alveri Alves 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:
Álgebras de Hopf
Extensões de Hopf-Ore
Álgebras de Hopf pontuadas
Palavras-chave em Inglês:
Hopf algebras
Hopf-Ore extensions
Pointed Hopf algebras
Área do conhecimento CNPq:
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Link de acesso: http://repositorio.ufsm.br/handle/1/19102
Resumo: In this work we will treat, in particular, of the Hopf algebras and Hopf-Ore extensions. One of ours main goals is to prove a theorem that characterizes when a Hopf algebra R is a extension of Hopf-Ore of a Hopf algebra H. This theorem has been proved by A. N. Panov in (PANOV, 2003). Furthermore, we use iterated extensions of Hopf-Ore to build Hopf algebras pointed and co-Frobenius and with that give a negative answer to the tenth Kaplansky’s conjecture.
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spelling 2019-12-04T22:21:44Z2019-12-04T22:21:44Z2019-06-28http://repositorio.ufsm.br/handle/1/19102In this work we will treat, in particular, of the Hopf algebras and Hopf-Ore extensions. One of ours main goals is to prove a theorem that characterizes when a Hopf algebra R is a extension of Hopf-Ore of a Hopf algebra H. This theorem has been proved by A. N. Panov in (PANOV, 2003). Furthermore, we use iterated extensions of Hopf-Ore to build Hopf algebras pointed and co-Frobenius and with that give a negative answer to the tenth Kaplansky’s conjecture.Neste trabalho trataremos em particular das noções de álgebras de Hopf e de extensões de Hopf-Ore. Um dos nossos principais objetivos é provar um teorema que caracteriza quando uma álgebra de Hopf R é uma extensão de Hopf-Ore de uma álgebra de Hopf H. Este teorema foi demonstrado por A. N. Panov em (PANOV, 2003). Além disso, usamos iteradas extensões de Hopf-Ore para construir álgebras de Hopf pontuadas e co-Frobenius e com isso dar uma resposta negativa a décima conjectura de Kaplansky.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPESporUniversidade 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/openAccessÁlgebras de HopfExtensões de Hopf-OreÁlgebras de Hopf pontuadasHopf algebrasHopf-Ore extensionsPointed Hopf algebrasCNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICAExtensões de Hopf-Ore e a décima conjectura de KaplanskyHopf-Ore extensions and Kaplansky’s tenth conjectureinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisFlôres, Daiana Aparecida da Silvahttp://lattes.cnpq.br/8009247848619231Morgado, Andreahttp://lattes.cnpq.br/8469234697525637Sant'Ana, Alveri Alveshttp://lattes.cnpq.br/3221572278471780http://lattes.cnpq.br/6953841362234680Garcia, Christian Michel da Cunha100100000008600522f3c30-9fb4-43e9-a334-f75108196474fd053ca2-e495-4041-87a3-af62c4c35586d4e7a0cd-dea1-412e-b279-97f69317ef65ee38394b-b1a0-4c5a-aa1e-ce2affe9e811reponame:Manancial - Repositório Digital da UFSMinstname:Universidade Federal de Santa Maria (UFSM)instacron:UFSMORIGINALDIS_PPGMATEMATICA_2019_GARCIA_CHRISTIAN.pdfDIS_PPGMATEMATICA_2019_GARCIA_CHRISTIAN.pdfDissertação de Mestradoapplication/pdf878821http://repositorio.ufsm.br/bitstream/1/19102/1/DIS_PPGMATEMATICA_2019_GARCIA_CHRISTIAN.pdf9007bf65b07c12348929b597973e440cMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; 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dc.title.por.fl_str_mv Extensões de Hopf-Ore e a décima conjectura de Kaplansky
dc.title.alternative.eng.fl_str_mv Hopf-Ore extensions and Kaplansky’s tenth conjecture
title Extensões de Hopf-Ore e a décima conjectura de Kaplansky
spellingShingle Extensões de Hopf-Ore e a décima conjectura de Kaplansky
Garcia, Christian Michel da Cunha
Álgebras de Hopf
Extensões de Hopf-Ore
Álgebras de Hopf pontuadas
Hopf algebras
Hopf-Ore extensions
Pointed Hopf algebras
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Extensões de Hopf-Ore e a décima conjectura de Kaplansky
title_full Extensões de Hopf-Ore e a décima conjectura de Kaplansky
title_fullStr Extensões de Hopf-Ore e a décima conjectura de Kaplansky
title_full_unstemmed Extensões de Hopf-Ore e a décima conjectura de Kaplansky
title_sort Extensões de Hopf-Ore e a décima conjectura de Kaplansky
author Garcia, Christian Michel da Cunha
author_facet Garcia, Christian Michel da Cunha
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.referee1.fl_str_mv Morgado, Andrea
dc.contributor.referee1Lattes.fl_str_mv http://lattes.cnpq.br/8469234697525637
dc.contributor.referee2.fl_str_mv Sant'Ana, Alveri Alves
dc.contributor.referee2Lattes.fl_str_mv http://lattes.cnpq.br/3221572278471780
dc.contributor.authorLattes.fl_str_mv http://lattes.cnpq.br/6953841362234680
dc.contributor.author.fl_str_mv Garcia, Christian Michel da Cunha
contributor_str_mv Flôres, Daiana Aparecida da Silva
Morgado, Andrea
Sant'Ana, Alveri Alves
dc.subject.por.fl_str_mv Álgebras de Hopf
Extensões de Hopf-Ore
Álgebras de Hopf pontuadas
topic Álgebras de Hopf
Extensões de Hopf-Ore
Álgebras de Hopf pontuadas
Hopf algebras
Hopf-Ore extensions
Pointed Hopf algebras
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Hopf algebras
Hopf-Ore extensions
Pointed Hopf algebras
dc.subject.cnpq.fl_str_mv CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work we will treat, in particular, of the Hopf algebras and Hopf-Ore extensions. One of ours main goals is to prove a theorem that characterizes when a Hopf algebra R is a extension of Hopf-Ore of a Hopf algebra H. This theorem has been proved by A. N. Panov in (PANOV, 2003). Furthermore, we use iterated extensions of Hopf-Ore to build Hopf algebras pointed and co-Frobenius and with that give a negative answer to the tenth Kaplansky’s conjecture.
publishDate 2019
dc.date.accessioned.fl_str_mv 2019-12-04T22:21:44Z
dc.date.available.fl_str_mv 2019-12-04T22:21:44Z
dc.date.issued.fl_str_mv 2019-06-28
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/1/19102
url http://repositorio.ufsm.br/handle/1/19102
dc.language.iso.fl_str_mv por
language por
dc.relation.cnpq.fl_str_mv 100100000008
dc.relation.confidence.fl_str_mv 600
dc.relation.authority.fl_str_mv 522f3c30-9fb4-43e9-a334-f75108196474
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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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institution UFSM
reponame_str Manancial - Repositório Digital da UFSM
collection Manancial - Repositório Digital da UFSM
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