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 $T_{poly}({\mathbb R}^d)$.
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Submitted on : Friday, July 11, 2008 - 12:33:35 PM
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  • HAL Id : hal-00294976, version 1
  • ARXIV : 0807.1829

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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⟩

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