# Cohomologie de Chevalley des graphes vectoriels

Abstract : The space of smotth functions and vector fields on $\R^d$ is a Lie subalgebra of the (graded) Lie algebra $T_{poly}(\R^d)$, equipped with the Scouten bracket. In this paper, we compute the cohomology of this subalgebra for the adjoint representation in $T_{poly}(\R^d)$, restricting ourselves to the case of cochains defined with purely aerial Kontsevich's graphs, as in [AGM]. We find results which are very similar to the classical Gelfand-Fuchs and de Wilde-Lecomte one.
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https://hal.archives-ouvertes.fr/hal-00005791
Contributor : Didier Arnal <>
Submitted on : Monday, July 4, 2005 - 12:23:57 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
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### Citation

Walid Aloulou, Didier Arnal, Ridha Chatbouri. Cohomologie de Chevalley des graphes vectoriels. Pacific Journal of Mathematics, 2007, 229 (2), pp.257-292. ⟨hal-00005791⟩

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