Deformation quantization of integrable systems
Georgy Sharygin
Lomonosov Moscow State University and ITEP, Moscow, RussiaDmitry 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