2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75664The 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.Quantum Algebra53D55 ; 17B56 ; 05Cxxtext