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

Mudrov, A.

doi:10.1090/S1061-0022-07-00974-0

On quantization of the Semenov-Tian-Shansky Poisson bracket on simple algebraic groups
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by A. Mudrov

St. Petersburg Math. J. 18 (2007), 797-808

DOI: https://doi.org/10.1090/S1061-0022-07-00974-0

Published electronically: August 10, 2007

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Abstract:

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

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