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# Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley-Harrison

DOI:ARXIV:0807.1829
Source: OAI

ABSTRACT The fundamental example of Gerstenhaber algebra is the space $T_{poly}({\mathbb R}^d)$ of polyvector fields on $\mathbb{R}^d$, equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping $G_\infty$ algebra of a Gerstenhaber algebra $\mathcal{G}$. This structure gives us a definition of the Chevalley-Harrison cohomology operator for $\mathcal{G}$. We finally show the nontriviality of a Chevalley-Harrison cohomology group for a natural Gerstenhaber subalgebra in $T_{poly}({\mathbb R}^d)$.

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### Keywords

Chevalley-Harrison cohomology group

Chevalley-Harrison cohomology operator

Gerstenhaber algebra $\mathcal{G}$

natural Gerstenhaber subalgebra

nontriviality

wedge product