Isaac Newton Institute for Mathematical Sciences

Obstructions for the deformation quantisation of integrable systems

Presenter: Georgy Sharygin (ITEP, Moscow and MSU, Moscow)

Co-author: Dmitry Talalaev (ITEP, Moscow and MSU, Moscow)

Abstract

In this work we discuss a construction, providing sufficient conditions for the existence of a deformation quantisation of a Poisson algebra, which preserves the commutativity of a subalgebra in it (if this subalgebra is Poisson-commutative). These conditions are expressible in the terms of vanishing of certain classes in the Poisson homology of the subalgebra with coefficients in a module. They are the generaisations of the similar classes of Garay and van Straten.

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