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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| Autores principales: | , |
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| Formato: | JOUR |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00218693_v390_n_p56_Farinati |
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| Sumario: | 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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