Classification of equivariant star products on symplectic manifolds. (English) Zbl 1341.53123

Reichert, Thorsten; Waldmann, Stefan

Lett. Math. Phys. 106, No. 5, 675-692 (2016).

This paper classifies invariant star products with quantum momentum maps on symplectic manifolds. First, the authors recall basic definitions and results about invariant star products and quantum momentum maps. Then the construction of Fedosov is also briefly recalled. A bijection between the equivalence classes and the formal series in the second equivariant cohomology is established. This result allows to determine whether two given pairs of star products and corresponding quantum momentum maps are equivariantly equivalent.

Reviewer: Angela Gammella-Mathieu (Metz)

MSC:

53D55	Deformation quantization, star products
53D05	Symplectic manifolds (general theory)

Keywords:

invariant star product, deformation quantization; Fedosov construction; quantum momentum map; equivariant cohomoogy

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