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

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 $T_{poly}({\mathbb R}^d)$.
Mots-clés :
Document type :
Journal articles

Cited literature [10 references]

https://hal.archives-ouvertes.fr/hal-00294976
Contributor : Didier Arnal <>
Submitted on : Friday, July 11, 2008 - 12:33:35 PM
Last modification on : Friday, June 8, 2018 - 2:50:07 PM
Long-term archiving on : Friday, May 28, 2010 - 11:25:05 PM

### Files

algGerst.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-00294976, version 1
• ARXIV : 0807.1829

### Citation

Walid Aloulou, Didier Arnal, Ridha Chatbouri. Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley-Harrison. Bulletin des Sciences Mathématiques, Elsevier, 2009, 133 (1), pp.1-50. ⟨hal-00294976⟩

Record views