Classification of deformation quantization algebroids on complex symplectic manifolds
Abstract
Description
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 τ. 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 τ^-1.
17 pages; section 6 removed (see "Uniqueness of quantization of complex contact manifolds") and minor changes
17 pages; section 6 removed (see "Uniqueness of quantization of complex contact manifolds") and minor changes