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Lie quasi-bialgebras are natural generalisations of Lie bialgebras introducedby 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 anisomorphism of D-modules between \Lambda D and End(\Lambda G), D acting on\Lambda D by the adjoint action.

Quasi-big\`ebres de Lie et cohomologie d'alg\`ebre de Lie