Chevalley Cohomology for linear graphs

Abstract

The space of linear polyvector fields on \(\mathbb{R}^d\) is a Lie subalgebra of the (graded) Lie algebra \(T_{\rm poly}(\mathbb{R}^d)\), equipped with the Schouten bracket. In this paper, we compute the cohomology of this subalgebra for the adjoint representation in \(T_{\rm poly}(\mathbb{R}^d)\), restricting ourselves to the case of cochains defined with purely aerial Kontsevich’s graphs, as in Pac. J. Math. 218(2):201–239, 2005. We find a result which is very similar to the cohomology for the vector case Pac. J. Math. 229(2):257–292, 2007.