On quantizations of complex contact manifolds
Algebraic Geometry
2015-03-13 v3 Quantum Algebra
Abstract
A (holomorphic) quantization of a complex contact manifold is a filtered algebroid stack which is locally equivalent to the ring E of microdifferential operators and which has trivial graded. The existence of a canonical quantization has been proved by Kashiwara. In this paper we consider the classification problem, showing that the above quantizations are classified by the first cohomology group with values in a certain sheaf of homogeneous forms. Secondly, we consider the problem of existence and classification for quantizations given by algebras.
Keywords
Cite
@article{arxiv.1211.4820,
title = {On quantizations of complex contact manifolds},
author = {Pietro Polesello},
journal= {arXiv preprint arXiv:1211.4820},
year = {2015}
}
Comments
Final published version (with a slightly different title from the previous arXiv versions)