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Donin, Joseph

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

Adv. Math. 127, No. 1, 73-93 (1997).
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.
Reviewer: L.G.Makar-Limanov (Detroit)

Cited in 2 Documents

MSC:

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

Keywords:

Poisson brackets; deformation quantization; field of zero characteristic

Citations:

Zbl 0737.47042
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\textit{J. Donin}, Adv. Math. 127, No. 1, 73--93 (1997; Zbl 0931.53040)
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