ИСТИНА

Let M be a Poisson manifold. As one knows according to Kontsevich’s result there always exists a deformation quantization of the algebra of smooth functions on M. Suppose now that f1, . . . , fn are Poisson commuting functions on M. In my talk I shall discuss the question, whether it is possible to extend these functions to commuting elements in the deformed algebra. I will describe few old and new cohomological obstructions for this and discuss relations between them; I will also give few examples of such systems and their quantizations.