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Preprints Archive: Abstract of IC2010016 (2010)

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Quasi-bigebres de Lie et cohomologie d'algebre de Lie

by Momo Bangoura

Document info: Pages 22, Figures 0.

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

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