On quantization of Semenov-Tian-Shansky Poisson bracket on simple algebraic groups
نویسندگان
چکیده
Let G be a simple complex algebraic group equipped with a factorizable Poisson Lie structure. Let U~(g) be the corresponding quantum group. We study U~(g)-equivariant quantization C~[G] of the affine coordinate ring C[G] along the Semenov-Tian-Shansky Poisson Lie bracket. For a simply connected group G we prove an analog of the KostantRichardson theorem stating that C~[G] is a free module over its center.
منابع مشابه
On Quantization of the Semenov-tian-shansky Poisson Bracket on Simple Algebraic Groups
Let G be a simple complex factorizable Poisson algebraic group. Let U (g) be the corresponding quantum group. We study the U (g)-equivariant quantization C [G] of the affine coordinate ring 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 C [G] is a free module over its center.
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