Classification of deformation quantization algebroids on complex symplectic manifolds
Algebraic Geometry
2007-05-23 v2 Symplectic Geometry
Abstract
Deformation quantization algebroids over a complex symplectic manifold X are locally given by rings of WKB operators, that is, microdifferential operators with an extra central parameter \tau. In this paper, we will show that such algebroids are classified by H^2(X;k^*), where k^* is a subgroup of the group of invertible formal Laurent series in \tau^-1.
Cite
@article{arxiv.math/0503400,
title = {Classification of deformation quantization algebroids on complex symplectic manifolds},
author = {Pietro Polesello},
journal= {arXiv preprint arXiv:math/0503400},
year = {2007}
}
Comments
17 pages; section 6 removed (see "Uniqueness of quantization of complex contact manifolds") and minor changes