Odd-quadratic Lie superalgebras with a weak filiform module as an odd part
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/100188 https://doi.org/10.1016/j.laa.2022.04.013 |
Resumo: | The aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that is a weak filiform -module (weak filiform type). We introduce this concept after having proved that the unique non-zero odd-quadratic Lie superalgebra with a filiform -module is the abelian 2-dimensional Lie superalgebra such that . Let us note that in this context the role of the center of is crucial. Thus, we obtain an inductive description of odd-quadratic Lie superalgebras of weak filiform type via generalized odd double extensions. Moreover, we obtain the classification, up to isomorphism, for the smallest possible dimensions, that is, six and eight. |
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Odd-quadratic Lie superalgebras with a weak filiform module as an odd partLie superalgebrasOdd-invariant scalar productDouble extensionsWeak filiformNilpotentThe aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that is a weak filiform -module (weak filiform type). We introduce this concept after having proved that the unique non-zero odd-quadratic Lie superalgebra with a filiform -module is the abelian 2-dimensional Lie superalgebra such that . Let us note that in this context the role of the center of is crucial. Thus, we obtain an inductive description of odd-quadratic Lie superalgebras of weak filiform type via generalized odd double extensions. Moreover, we obtain the classification, up to isomorphism, for the smallest possible dimensions, that is, six and eight.The first author was supported by the Centre for Mathematics of the University of Coimbra - UIDB/00324/2020, funded by the Portuguese Government through FCT/MCTES. Third author was supported by Junta de Extremadura and Fondo Europeo de Desarrollo Regional (GR21005 and IB18032) and by Agencia Estatal de Investigación (Spain), grant PID2020-115155GB-I00 (European FEDER support included, UE). Fourth author was supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banach’ and by the PAI with project number FQM298.Elsevier2022info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/100188http://hdl.handle.net/10316/100188https://doi.org/10.1016/j.laa.2022.04.013eng00243795Barreiro, ElisabeteBenayadi, SaïdNavarro, Rosa M.Sánchez, José M.info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-05-23T21:06:12Zoai:estudogeral.uc.pt:10316/100188Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T21:17:38.071757Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
title |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
spellingShingle |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part Barreiro, Elisabete Lie superalgebras Odd-invariant scalar product Double extensions Weak filiform Nilpotent |
title_short |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
title_full |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
title_fullStr |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
title_full_unstemmed |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
title_sort |
Odd-quadratic Lie superalgebras with a weak filiform module as an odd part |
author |
Barreiro, Elisabete |
author_facet |
Barreiro, Elisabete Benayadi, Saïd Navarro, Rosa M. Sánchez, José M. |
author_role |
author |
author2 |
Benayadi, Saïd Navarro, Rosa M. Sánchez, José M. |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Barreiro, Elisabete Benayadi, Saïd Navarro, Rosa M. Sánchez, José M. |
dc.subject.por.fl_str_mv |
Lie superalgebras Odd-invariant scalar product Double extensions Weak filiform Nilpotent |
topic |
Lie superalgebras Odd-invariant scalar product Double extensions Weak filiform Nilpotent |
description |
The aim of this work is to study a very special family of odd-quadratic Lie superalgebras such that is a weak filiform -module (weak filiform type). We introduce this concept after having proved that the unique non-zero odd-quadratic Lie superalgebra with a filiform -module is the abelian 2-dimensional Lie superalgebra such that . Let us note that in this context the role of the center of is crucial. Thus, we obtain an inductive description of odd-quadratic Lie superalgebras of weak filiform type via generalized odd double extensions. Moreover, we obtain the classification, up to isomorphism, for the smallest possible dimensions, that is, six and eight. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/100188 http://hdl.handle.net/10316/100188 https://doi.org/10.1016/j.laa.2022.04.013 |
url |
http://hdl.handle.net/10316/100188 https://doi.org/10.1016/j.laa.2022.04.013 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
00243795 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799134071492706304 |