Cohomologie de Chevalley des graphes vectoriels

Abstract

The space of smotth functions and vector fields on ${\mathbb{R}}^d$ is a Lie subalgebra of the (graded) Lie algebra $T\_poly({\mathbb{R}}^d)$, equipped with the Scouten bracket. In this paper, we compute the cohomology of this subalgebra for the adjoint representation in $T\_poly({\mathbb{R}}^d)$, 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.