A note on quantization of complex symplectic manifolds

TL;DR

This paper introduces a canonical quantization algebroid for complex symplectic manifolds, extending deformation-quantization concepts with a non-central deformation parameter, and explores the resulting categorical structures.

Contribution

It constructs a new canonical quantization algebroid for complex symplectic manifolds with a non-central deformation parameter, expanding the framework of deformation quantization.

Findings

The quantization category is a Calabi-Yau category of dimension 1 + dim X.

The construction generalizes existing deformation-quantization algebroids.

The approach applies to compact complex symplectic manifolds.

Abstract

To a complex symplectic manifold X we associate a canonical quantization algebroid. Our construction is similar to that of Polesello-Schapira's deformation-quantization algebroid, but the deformation parameter is no longer central. If X is compact, the triangulated category of regular holonomic quantization modules is a linear complex Calabi-Yau category of dimension 1 + dim X.