Cohomologie de Chevalley des graphes ascendants

Walid Aloulou (1, 2) , Didier Arnal (2) , Ridha Chatbouri (1, 2)

1 Département de Mathématiques, Unité de recherche Physique Mathématique
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

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.

Mots clés: Graphes de Kontsevitch; cohomolgie de Chevalley

Domaines: Algèbres quantiques [math.QA]

Walid Aloulou, Didier Arnal, Ridha Chatbouri. Cohomologie de Chevalley des graphes ascendants. 2010. ⟨hal-00465530⟩