On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups

Details On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups

2004-12-18

arxiv.org/abs/math/0412360v2

Mathematics

Quantum Algebra

17 pages, an error in a proof in Section 6.1 corrected

Scientific paper

Let $G$ be a simple complex factorizable Poisson Lie algebraic group. Let $\U_\hbar(\g)$ be the corresponding quantum group. We study $\U_\hbar(\g)$-equivariant quantization $\C_\hbar[G]$ of the affine coordinate ring $\C[G]$ along the Semenov-Tian-Shansky bracket. For a simply connected group $G$ we prove an analog of the Kostant-Richardson theorem stating that $\C_\hbar[G]$ is a free module over its center.

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