A New Approach to Leibniz Bialgebras

Detalhes bibliográficos
Autor(a) principal: Barreiro, Elisabete
Data de Publicação: 2015
Outros Autores: Benayadi, Saïd
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/43767
https://doi.org/10.1007/s10468-015-9563-6
Resumo: A study of Leibniz bialgebras arising naturally through the double of Leibniz algebras analogue to the classical Drinfeld’s double is presented. A key ingredient of our work is the fact that the underline vector space of a Leibniz algebra becomes a Lie algebra and also a commutative associative algebra, when provided with appropriate new products. A special class of them, the coboundary Leibniz bialgebras, gives us the natural framework for studying the Yang-Baxter equation (YBE) in our context, inspired in the classical Yang-Baxter equation as well as in the associative Yang-Baxter equation. Results of the existence of coboundary Leibniz bialgebra on a symmetric Leibniz algebra under certain conditions are obtained. Some interesting examples of coboundary Leibniz bialgebras are also included. The final part of the paper is dedicated to coboundary Leibniz bialgebra structures on quadratic Leibniz algebras.
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spelling A New Approach to Leibniz BialgebrasA study of Leibniz bialgebras arising naturally through the double of Leibniz algebras analogue to the classical Drinfeld’s double is presented. A key ingredient of our work is the fact that the underline vector space of a Leibniz algebra becomes a Lie algebra and also a commutative associative algebra, when provided with appropriate new products. A special class of them, the coboundary Leibniz bialgebras, gives us the natural framework for studying the Yang-Baxter equation (YBE) in our context, inspired in the classical Yang-Baxter equation as well as in the associative Yang-Baxter equation. Results of the existence of coboundary Leibniz bialgebra on a symmetric Leibniz algebra under certain conditions are obtained. Some interesting examples of coboundary Leibniz bialgebras are also included. The final part of the paper is dedicated to coboundary Leibniz bialgebra structures on quadratic Leibniz algebras.Springer2015info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/43767http://hdl.handle.net/10316/43767https://doi.org/10.1007/s10468-015-9563-6https://doi.org/10.1007/s10468-015-9563-6enghttps://link.springer.com/article/10.1007/s10468-015-9563-6Barreiro, ElisabeteBenayadi, Saïdinfo: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:RCAAP2021-06-29T10:02:52Zoai:estudogeral.uc.pt:10316/43767Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:27.305311Repositório 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 A New Approach to Leibniz Bialgebras
title A New Approach to Leibniz Bialgebras
spellingShingle A New Approach to Leibniz Bialgebras
Barreiro, Elisabete
title_short A New Approach to Leibniz Bialgebras
title_full A New Approach to Leibniz Bialgebras
title_fullStr A New Approach to Leibniz Bialgebras
title_full_unstemmed A New Approach to Leibniz Bialgebras
title_sort A New Approach to Leibniz Bialgebras
author Barreiro, Elisabete
author_facet Barreiro, Elisabete
Benayadi, Saïd
author_role author
author2 Benayadi, Saïd
author2_role author
dc.contributor.author.fl_str_mv Barreiro, Elisabete
Benayadi, Saïd
description A study of Leibniz bialgebras arising naturally through the double of Leibniz algebras analogue to the classical Drinfeld’s double is presented. A key ingredient of our work is the fact that the underline vector space of a Leibniz algebra becomes a Lie algebra and also a commutative associative algebra, when provided with appropriate new products. A special class of them, the coboundary Leibniz bialgebras, gives us the natural framework for studying the Yang-Baxter equation (YBE) in our context, inspired in the classical Yang-Baxter equation as well as in the associative Yang-Baxter equation. Results of the existence of coboundary Leibniz bialgebra on a symmetric Leibniz algebra under certain conditions are obtained. Some interesting examples of coboundary Leibniz bialgebras are also included. The final part of the paper is dedicated to coboundary Leibniz bialgebra structures on quadratic Leibniz algebras.
publishDate 2015
dc.date.none.fl_str_mv 2015
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dc.type.driver.fl_str_mv info:eu-repo/semantics/article
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status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10316/43767
http://hdl.handle.net/10316/43767
https://doi.org/10.1007/s10468-015-9563-6
https://doi.org/10.1007/s10468-015-9563-6
url http://hdl.handle.net/10316/43767
https://doi.org/10.1007/s10468-015-9563-6
dc.language.iso.fl_str_mv eng
language eng
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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