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

A. Mudrov

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

Quantum Algebra 2007-05-23 v2

Authors: A. Mudrov

Abstract

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.

Keywords

poisson algebras poisson geometry algebraic group actions

Cite

@article{arxiv.math/0412360,
  title  = {On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups},
  author = {A. Mudrov},
  journal= {arXiv preprint arXiv:math/0412360},
  year   = {2007}
}

Comments

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

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

Abstract

Keywords

Cite

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