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Poisson bracket, deformed bracket and gauge group actions in Kontsevich deformation quantization. (English) Zbl 0981.53091
Summary: We express the difference between the Poisson bracket and a deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of the second derivative of the formality quasi-isomorphism. The counterpart in star products of the action of formal diffeomorphisms on Poisson formal bivector fields is also investigated.

MSC:
53D55 Deformation quantization, star products
16S80 Deformations of associative rings
53D17 Poisson manifolds; Poisson groupoids and algebroids
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