Cohomology of the Vector Fields Lie Algebra and Modules of Differential Operators on a Smooth Manifold |
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| Authors: | P B A Lecomte V Yu Ovsienko |
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| Institution: | (1) Institute de Mathématiques, Université de Liège, Sart Tilman, Grande Traverse, 12 (B 37), B-4000 Liège, Belgium;(2) Centre de Physique Théorique, C.N.R.S., Luminy – Case 907, F–13288 Marseille, Cedex 9, France |
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| Abstract: | Let M be a smooth manifold,
the space of polynomial on fibers functions on T*M (i.e., of symmetric contravariant tensor fields). We compute the first cohomology space of the Lie algebra, Vect(M), of vector fields on M with coefficients in the space of linear differential operators on
. This cohomology space is closely related to the Vect(M)-modules,
 (M), of linear differential operators on the space of tensor densities on M of degree . |
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| Keywords: | cohomology differential operators quantization |
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