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On the quantization of Poisson brackets. (English) Zbl 0931.53040

In this paper, which appeared considerably earlier than the famous preprint of M. Kontsevich “Formal quantization of Poisson manifolds”, the author introduces a rather wide class of Poisson brackets which can be quantized by an algebraic version of B. V. Fedosov’s method [Funct. Anal. Appl. 25, 184-194 (1991; Zbl 0737.47042)]. An interesting, purely algebraic consequence of these results is that any Poisson bracket on a field of zero characteristic can be quantized.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53D55 Deformation quantization, star products

Citations:

Zbl 0737.47042
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References:

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