Cohomology of the vector fields Lie algebra and modules of differential operators on a smooth manifold

摘要

Let M be a smooth manifold, S 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 S. This cohomology space is closely related to the Vect(M)-modules, D-lambda(M), of linear differential operators on the space of tensor densities on M of degree lambda. [References: 17]