PI-equivalência em álgebras graduadas simples
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/7911 |
Resumo: | This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we will show the following: Let G be a group, F an algebraically closed eld, and R = L g2G Rg a finite dimensional G-graded F-algebra such that the order of each finite subgroup of G is invertible in F. Then R is a G-graded simple algebra if and only if R is isomorphic, as graded algebra, to the tensor product C = Mn(F) F [H], where H is a nite subgroup of G, is a 2-cocycle in H, Mn(F) has an elementary G-grading, F [H] has a canonical grading and C has an induced G-grading by the tensor product. Based on this result, admitting the same assumptions and adding that G is an abelian group, we prove that two graded simple algebras satisfy the same graded identities if and only if they are isomorphic as graded algebras. |
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Naves, Fernando AugustoTalpo, Humberto Luizhttp://lattes.cnpq.br/1674689444257254http://lattes.cnpq.br/2387898216530288886e4cb2-c0e5-463a-8226-430fa2e60e862016-10-17T19:06:01Z2016-10-17T19:06:01Z2016-02-29NAVES, Fernando Augusto. PI-equivalência em álgebras graduadas simples. 2016. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7911.https://repositorio.ufscar.br/handle/ufscar/7911This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we will show the following: Let G be a group, F an algebraically closed eld, and R = L g2G Rg a finite dimensional G-graded F-algebra such that the order of each finite subgroup of G is invertible in F. Then R is a G-graded simple algebra if and only if R is isomorphic, as graded algebra, to the tensor product C = Mn(F) F [H], where H is a nite subgroup of G, is a 2-cocycle in H, Mn(F) has an elementary G-grading, F [H] has a canonical grading and C has an induced G-grading by the tensor product. Based on this result, admitting the same assumptions and adding that G is an abelian group, we prove that two graded simple algebras satisfy the same graded identities if and only if they are isomorphic as graded algebras.Este trabalho tem por objetivo dar uma descrição, sob certas hipóteses, das álgebras graduadas simples e demonstrar que elas são determinadas por suas identidades graduadas. Para isso, estudamos os artigos [3] e [19]. Precisamente mostraremos o seguinte: sejam G um grupo, F um corpo algebricamente fechado e R =Lg2GRg uma F-álgebra G-graduada de dimensão finita, tal que a ordem de todo subgrupo finito de G e invertível em F. Então R é uma álgebra G-graduada simples se, e somente se, R é isomorfa, como álgebra graduada, ao produto tensorial C = Mn(F) F[H], onde H e subgrupo finito de G, e um 2-cociclo em H, Mn(F) tem uma graduação elementar, F[H] tem uma graduação canônica e considera-se em C a G-graduação induzida pelo produto tensorial. Partindo deste resultado, admitindo as mesmas hipóteses e adicionando que G seja um grupo abeliano, provaremos que duas álgebras graduadas simples satisfazem as mesmas identidades graduadas se, e somente se, são isomorfas como álgebras graduadas.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarPI- álgebrasG-graduaçõesIdentidades polinomiaisIdentidades graduadasÁlgebras graduadas simplesG-gradingsPolynomial identitiesGraded identitiesGraded simple algebrasCIENCIAS EXATAS E DA TERRA::MATEMATICACIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRAPI-equivalência em álgebras graduadas simplesinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600d36b9ec5-6583-4a3a-a534-73d7ad1b9a2einfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALDissFAN.pdfDissFAN.pdfapplication/pdf767462https://repositorio.ufscar.br/bitstream/ufscar/7911/1/DissFAN.pdf05054cc8952eed4e120838068aee80d8MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/7911/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTDissFAN.pdf.txtDissFAN.pdf.txtExtracted texttext/plain143255https://repositorio.ufscar.br/bitstream/ufscar/7911/3/DissFAN.pdf.txt480c2c106f380d1b20bb25ed6b1954f5MD53THUMBNAILDissFAN.pdf.jpgDissFAN.pdf.jpgIM Thumbnailimage/jpeg5902https://repositorio.ufscar.br/bitstream/ufscar/7911/4/DissFAN.pdf.jpg8f77141368eb687b25422e9c8148c2afMD54ufscar/79112023-09-18 18:30:59.9oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:30:59Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
PI-equivalência em álgebras graduadas simples |
title |
PI-equivalência em álgebras graduadas simples |
spellingShingle |
PI-equivalência em álgebras graduadas simples Naves, Fernando Augusto PI- álgebras G-graduações Identidades polinomiais Identidades graduadas Álgebras graduadas simples G-gradings Polynomial identities Graded identities Graded simple algebras CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA |
title_short |
PI-equivalência em álgebras graduadas simples |
title_full |
PI-equivalência em álgebras graduadas simples |
title_fullStr |
PI-equivalência em álgebras graduadas simples |
title_full_unstemmed |
PI-equivalência em álgebras graduadas simples |
title_sort |
PI-equivalência em álgebras graduadas simples |
author |
Naves, Fernando Augusto |
author_facet |
Naves, Fernando Augusto |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/2387898216530288 |
dc.contributor.author.fl_str_mv |
Naves, Fernando Augusto |
dc.contributor.advisor1.fl_str_mv |
Talpo, Humberto Luiz |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1674689444257254 |
dc.contributor.authorID.fl_str_mv |
886e4cb2-c0e5-463a-8226-430fa2e60e86 |
contributor_str_mv |
Talpo, Humberto Luiz |
dc.subject.por.fl_str_mv |
PI- álgebras G-graduações Identidades polinomiais Identidades graduadas Álgebras graduadas simples |
topic |
PI- álgebras G-graduações Identidades polinomiais Identidades graduadas Álgebras graduadas simples G-gradings Polynomial identities Graded identities Graded simple algebras CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA |
dc.subject.eng.fl_str_mv |
G-gradings Polynomial identities Graded identities Graded simple algebras |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA |
description |
This work aims to give a description, under certain hypothesis, of the graded simple algebras and prove that they are determined by their graded identities. For this, we study the papers [3] and [19]. More precisely we will show the following: Let G be a group, F an algebraically closed eld, and R = L g2G Rg a finite dimensional G-graded F-algebra such that the order of each finite subgroup of G is invertible in F. Then R is a G-graded simple algebra if and only if R is isomorphic, as graded algebra, to the tensor product C = Mn(F) F [H], where H is a nite subgroup of G, is a 2-cocycle in H, Mn(F) has an elementary G-grading, F [H] has a canonical grading and C has an induced G-grading by the tensor product. Based on this result, admitting the same assumptions and adding that G is an abelian group, we prove that two graded simple algebras satisfy the same graded identities if and only if they are isomorphic as graded algebras. |
publishDate |
2016 |
dc.date.accessioned.fl_str_mv |
2016-10-17T19:06:01Z |
dc.date.available.fl_str_mv |
2016-10-17T19:06:01Z |
dc.date.issued.fl_str_mv |
2016-02-29 |
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 |
NAVES, Fernando Augusto. PI-equivalência em álgebras graduadas simples. 2016. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7911. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/7911 |
identifier_str_mv |
NAVES, Fernando Augusto. PI-equivalência em álgebras graduadas simples. 2016. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2016. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7911. |
url |
https://repositorio.ufscar.br/handle/ufscar/7911 |
dc.language.iso.fl_str_mv |
por |
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por |
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600 600 |
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d36b9ec5-6583-4a3a-a534-73d7ad1b9a2e |
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openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Matemática - PPGM |
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UFSCar |
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Universidade Federal de São Carlos Câmpus São Carlos |
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