Classification of invariant star products up to equivariant Morita equivalence on symplectic manifolds. (English) Zbl 1251.53057

Jansen, Stefan; Neumaier, Nikolai; Schaumann, Gregor; Waldmann, Stefan

Lett. Math. Phys. 100, No. 2, 203-236 (2012).

This paper gives the full classification of invariant star products up to equivariant Morita equivalence on a symplectic manifold. After some recalls about Morita theory and groupoid morphisms, the authors reformulate the criteria on the existence of quantum momentum maps in terms of equivariant cohomology. They then compute explicitly the equivariant Picard groupoid in terms of the Picard groupoid. They study in details the case of star products on symplectic manifolds. The main result of this paper enables the authors to classify the star-products up to Morita equivalence.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D55	Deformation quantization, star products
16D90	Module categories in associative algebras

Keywords:

deformation quantization; star products; momentum maps; Morita equivalence; Picard groupoids

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