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...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Recursos: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/66919 |
| Acesso em linha: | http://hdl.handle.net/11336/66919 |
| Access Level: | acceso abierto |
| Palavra-chave: | Derivations Extensions Lie Bialgebras https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| Resumo: | 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. |
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