Quasi-bigèbres de Lie et cohomologie d'algèbre de Lie

Details Quasi-bigèbres de Lie et cohomologie d'algèbre de Lie Quasi-bigèbres de Lie et cohomologie d'algèbre de Lie

2010-06-03

arxiv.org/abs/1006.0677v1

Mathematics

Representation Theory

Scientific paper

Lie quasi-bialgebras are natural generalisations of Lie bialgebras introduced by Drinfeld. To any Lie quasi-bialgebra structure of finite-dimensional (G, \mu, \gamma ,\phi ?), correspond one Lie algebra structure on D = G\oplus G*, called the double of the given Lie quasi-bialgebra. We show that there exist on \Lambda G, the exterior algebra of G, a D-module structure and we establish an isomorphism of D-modules between \Lambda D and End(\Lambda G), D acting on \Lambda D by the adjoint action.

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