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


Author: A. Mudrov
Original publication: Algebra i Analiz, tom 18 (2006), nomer 5.
Journal: St. Petersburg Math. J. 18 (2007), 797-808
MSC (2000): Primary 53Dxx; Secondary 20Gxx
DOI: https://doi.org/10.1090/S1061-0022-07-00974-0
Published electronically: August 10, 2007
MathSciNet review: 2301044
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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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Additional Information

A. Mudrov
Affiliation: Department of Mathematics, University of York, YO10 5DD, United Kingdom
Address at time of publication: St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia

DOI: https://doi.org/10.1090/S1061-0022-07-00974-0
Keywords: Poisson Lie manifolds, quantum groups, equivariant quantization
Received by editor(s): April 22, 2006
Published electronically: August 10, 2007
Additional Notes: This research is partially supported by the Emmy Noether Research Institute for Mathematics, the Minerva Foundation of Germany, the Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties” of the Israel Science Foundation, the CRDF grant RUM1-2622-ST-04, and by the RFBR grant no. 03-01-00593
Dedicated: Dedicated to the memory of Joseph Donin
Article copyright: © Copyright 2007 American Mathematical Society

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