Trivial central extensions of 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...

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Detalles Bibliográficos
Autor principal: Farinati, Marco Andres
Publicado: 2013
Materias:
Derivations
Extensions
Lie bialgebras
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v390_n_p56_Farinati
http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00218693_v390_n_p56_Farinati
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spelling paper:paper_00218693_v390_n_p56_Farinati2023-06-08T14:42:26Z Trivial central extensions of Lie bialgebras Farinati, Marco Andres 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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v390_n_p56_Farinati 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)
topic Derivations
Extensions
Lie bialgebras
spellingShingle Derivations
Extensions
Lie bialgebras
Farinati, Marco Andres
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.
author Farinati, Marco Andres
author_facet Farinati, Marco Andres
author_sort Farinati, Marco Andres
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 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v390_n_p56_Farinati
http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati
work_keys_str_mv AT farinatimarcoandres trivialcentralextensionsofliebialgebras
_version_ 1768542065575067648

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