Trivial central extensions of Lie bialgebras

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From a Lie algebra g satisfying Z(g)=0 and Λ2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×K{double-struck} in terms of Lie bialgebra structures on g (not necessarily factorizable nor quasi-triangular) and its biderivations...

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Autores principales: Farinati, M.A., Jancsa, A.P.
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: 2013
Materias:
Derivations
Extensions
Lie bialgebras
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paperaa:paper_00218693_v390_n_p56_Farinati
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spelling paperaa:paper_00218693_v390_n_p56_Farinati2023-06-12T16:42:29Z Trivial central extensions of Lie bialgebras J. Algebra 2013;390:56-76 Farinati, M.A. Jancsa, A.P. Derivations Extensions Lie bialgebras From a Lie algebra g satisfying Z(g)=0 and Λ2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×K{double-struck} in terms of Lie bialgebra structures on g (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field K of characteristic different form 2, 3. If moreover, [g,g]=g, then we describe also all Lie bialgebra structures on extensions L=g×K{double-struck}n. In interesting cases we characterize the Lie algebra of biderivations. © 2013 Elsevier Inc. Fil:Farinati, M.A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion application/pdf eng info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
language Inglés
orig_language_str_mv eng
topic Derivations
Extensions
Lie bialgebras
spellingShingle Derivations
Extensions
Lie bialgebras
Farinati, M.A.
Jancsa, A.P.
Trivial central extensions of Lie bialgebras
topic_facet Derivations
Extensions
Lie bialgebras
description From a Lie algebra g satisfying Z(g)=0 and Λ2(g)g=0 (in particular, for g semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form L=g×K{double-struck} in terms of Lie bialgebra structures on g (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field K of characteristic different form 2, 3. If moreover, [g,g]=g, then we describe also all Lie bialgebra structures on extensions L=g×K{double-struck}n. In interesting cases we characterize the Lie algebra of biderivations. © 2013 Elsevier Inc.
format Artículo
Artículo
publishedVersion
author Farinati, M.A.
Jancsa, A.P.
author_facet Farinati, M.A.
Jancsa, A.P.
author_sort Farinati, M.A.
title Trivial central extensions of Lie bialgebras
title_short Trivial central extensions of Lie bialgebras
title_full Trivial central extensions of Lie bialgebras
title_fullStr Trivial central extensions of Lie bialgebras
title_full_unstemmed Trivial central extensions of Lie bialgebras
title_sort trivial central extensions of lie bialgebras
publishDate 2013
url http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati
work_keys_str_mv AT farinatima trivialcentralextensionsofliebialgebras
AT jancsaap trivialcentralextensionsofliebialgebras
_version_ 1769810266365624320

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