Аннотация:In this short note I discuss the problem, if it is possible to extend
the action of a Lie algebra g of Poisson vector fields on a Poisson manifold
M, π (here π is the Poisson bivector) to an action of the same Lie
algebra on the deformation quantization of the algebra C∞(M) by differentiations.
In the paper I give a list of cohomological obstructions,
(taking values in Hochschild and Lichnerowicz-Poisson cohomology of
M), that vanish iff such deformation of g exists.