XXXVII Workshop on Geometric Methods in Physics | 1-7.07.2018 |

VII School on Geometry and Physics | 25-29.06.2018 |

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## Georgy Sharygin## The commuting elements in deformation of Poisson manifoldsLet $M$ 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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University of Bialystok |

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