Algèbres et cogèbres de Gerstenhaber et cohomologie de Chevalley-Harrison |
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| Authors: | Walid Aloulou Didier Arnal |
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| Affiliation: | a Département de Mathématiques, Unité de Recherche Physique Mathématique, Faculté des Sciences de Monastir, Avenue de l'environnement, 5019 Monastir, Tunisie
b Institut de Mathématiques de Bourgogne, UMR CNRS 5584, Université de Bourgogne, U.F.R. Sciences et Techniques, B.P. 47870, F-21078 Dijon Cedex, France |
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| Abstract: | The fundamental example of Gerstenhaber algebra is the space Tpoly(Rd) of polyvector fields on Rd, equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping G∞ algebra of a Gerstenhaber algebra G. This structure gives us a definition of the Chevalley-Harrison cohomology operator for G. We finally show the nontriviality of a Chevalley-Harrison cohomology group for a natural Gerstenhaber subalgebra in Tpoly(Rd). |
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| Keywords: | 18G55 16W30 16E45 53D55 |
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