Classification of Equivariant Star Products on Symplectic Manifolds

TL;DR

This paper provides a refined classification of invariant star products with quantum momentum maps on symplectic manifolds using equivariant cohomology, establishing a bijection with formal series in second equivariant cohomology.

Contribution

It introduces an equivariant characteristic class for classifying invariant star products with quantum momentum maps, refining previous classifications.

Findings

Classification via equivariant characteristic class

Bijection with formal series in second equivariant cohomology

Refined understanding of quantum momentum maps

Abstract

In this note we classify invariant star products with quantum momentum maps on symplectic manifolds by means of an equivariant characteristic class taking values in the equivariant cohomology. We establish a bijection between the equivalence classes and the formal series in the second equivariant cohomology, thereby giving a refined classification which takes into account the quantum momentum map as well.