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Covariant star-products. (English) Zbl 0839.53025
The author presents an elementary proof of the existence theorem for \(*\)-products on a symplectic manifold originally due to M. de Wilde and P. B. A. Lecomte [Lett. Math. Phys. 7, 235-241 (1983; Zbl 0514.53031)]. The exposition is also based on unpublised work by Lecomte and de Wilde. Moreover, the proof and the result are specialized to the case of the coadjoint orbit in the dual of a Lie algebra endowed with its canonical symplectic structure if this allows a maximal isotropic subspace.

MSC:
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
17B37 Quantum groups (quantized enveloping algebras) and related deformations
53D50 Geometric quantization
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