Cohomologie de Chevalley des graphes vectoriels

Details Cohomologie de Chevalley des graphes vectoriels Cohomologie de Chevalley des graphes vectoriels

2005-07-04

arxiv.org/abs/math/0507058v1

Mathematics

Quantum Algebra

Scientific paper

The 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.

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