Deformation quantization of integrable systems

  • Georgy Sharygin

    Lomonosov Moscow State University and ITEP, Moscow, Russia
  • Dmitry Talalaev

    Lomonosov Moscow State University and ITEP, Moscow, Russia

Abstract

In this paper we address the following question: is it always possible to choose a deformation quantization of a Poisson algebra so that certain Poisson-commutative subalgebra in it remains commutative? We define a series of cohomological obstructions to this, that take values in the Hochschild cohomology of with coefficients in . In some particular case of the pair we reduce these classes to the classes of the Poisson relative cohomology of the Hochschild cohomology. We show, that in the case, when the algebra is polynomial, these obstructions coincide with the previously known ones, those which were defined by Garay and van Straten.

Cite this article

Georgy Sharygin, Dmitry Talalaev, Deformation quantization of integrable systems. J. Noncommut. Geom. 11 (2017), no. 2, pp. 741–756

DOI 10.4171/JNCG/11-2-9