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Cohomologie de
Chevalley des graphes vectoriels
Walid Aloulou, Didier Arnal and Ridha Chatbouri |
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Vol. 229 (2007), No. 2, 257–292
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Abstract |
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The space of smooth functions and vector fields on ℝd is a Lie subalgebra of the (graded) Lie algebra Tpoly(ℝd), equipped with the Scouten bracket. Here we compute the cohomology of this subalgebra for the adjoint representation in Tpoly(ℝd), restricting ourselves to the case of cochains defined with purely aerial Kontsevich graphs, as in Arnal, Gammella and Masmoudi, Pacific Journal of Mathematics 218 (2005), 201–239. We find results very similar to the classical result of Gelfand–Fuks and those of De Wilde–Lecomte. |
Keywords
formality, vector graph, Chevalley cohomology
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Mathematical Subject Classification 2000
Primary: 17B56
Secondary: 53D55, 05C99
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Milestones
Received: 4 July 2005
Accepted: 4 May 2006
Published: 1 February 2007
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Authors |
| Walid Aloulou | |
| Département de Mathématiques Unité de Recherche Physique Mathématique Faculté des Sciences de Monastir Avenue de l’environnement 5019 Monastir Tunisie |
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| Didier Arnal | |
| 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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| Ridha Chatbouri | |
| Département de Mathématiques Unité de Recherche Physique Mathématique Faculté des Sciences de Monastir Avenue de l’environnement 5019 Monastir Tunisie |
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