|XXXVII Workshop on Geometric Methods in Physics||1-7.07.2018|
|VII School on Geometry and Physics||25-29.06.2018|
The commuting elements in deformation of Poisson manifolds
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 $f_1,\dots,f_n$ 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.
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