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Survey of the Deformation Quantization of Commutative Families

  • G. SharyginEmail author
  • A. Konyaev
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 273)

Abstract

In this survey chapter we discuss various approaches and known results, concerning the following question: when is it possible to find a commutative extension of a Poisson-commutative subalgebra in \(C^\infty (X)\) (where X is a Poisson manifold) to a commutative subalgebra in the deformation quantization of X, the algebra \(\mathscr {A}(X)\). A case of particular interest, which we consider with certain detail is the situation, when \(X=\mathfrak g^*\) and the commutative subalgebra is constructed by the argument shift method.

Keywords

Deformation quantization Poisson commutative subalgefbras (Quantum) integrable systems 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of Mechanics and Mathematics“Lomonosov” Moscow State UniversityMoscowRussia

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