Classification of deformation quantization algebroids on complex symplectic manifolds

Pietro Polesello

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Classification of deformation quantization algebroids on complex symplectic manifolds

Pietro Polesello

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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 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.

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Pietro Polesello. 2005-12-21. Classification of deformation quantization algebroids on complex symplectic manifolds. https://arxiv.org/abs/math/0503400

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