Cohomologie de Chevalley des graphes ascendants

Abstract

The space $T_{poly}({\mathbb{R}}^d)$ of all tensor fields on ${\mathbb{R}}^d$, equipped with the Schouten bracket is a Lie algebra. The subspace of ascending tensors is a Lie subalgebra of $T_{poly}({\mathbb{R}}^d)$. In this paper, we compute the cohomology of the adjoint representations of this algebra (in itself and $T_{poly}({\mathbb{R}}^d)$), when we restrict ourselves to cochains defined by aerial Kontsevitch's graphs like in our previous work (Pacific J of Math, vol 229, no 2, (2007) 257-292). As in the vectorial graphs case, the cohomology is freely generated by all the products of odd wheels.