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

MSC:
53D55 Deformation quantization, star products
53D05 Symplectic manifolds, general
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