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arXiv · 1003.4191

Cohomologie de Chevalley des graphes ascendants

Walid Aloulou·Didier Arnal·Ridha Chatbouri
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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.

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Walid Aloulou, Didier Arnal, Ridha Chatbouri. 2010-03-22. Cohomologie de Chevalley des graphes ascendants. https://arxiv.org/abs/1003.4191

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