Classification and Reduction of Homogeneous Star Products

TL;DR

This paper classifies homogeneous star products on duals of Lie algebroids using cohomology and extends the classification to compatible quantizations, showing that quantization commutes with reduction.

Contribution

It introduces a classification framework for homogeneous star products on Lie algebroid duals and extends it to projectable star products compatible with reduction.

Findings

Classification of homogeneous star products via Lie algebroid cohomology

Extension to projectable star products compatible with reduction

Quantization commutes with reduction in this setting

Abstract

We present a classification of homogeneous star products on duals of Lie algebroids in terms of the second Lie algebroid cohomology. Moreover, we extend this classification to projectable star products, i.e., to quantizations compatible with (coisotropic) reduction. This implies that quantization commutes with reduction in the considered setting.