Quantization of Poisson algebraic groups and Poisson homogeneous spaces

Abstract

This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the second part we apply our techniques of quantization to obtain some nontrivial examples of quantization of Poisson homogeneous spaces.

9 pages, amstex. The revised version contains a new reference

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