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June 2013 Manin Triples and Differential Operators on Quantum Groups
Toshiyuki TANISAKI
Tokyo J. Math. 36(1): 49-83 (June 2013). DOI: 10.3836/tjm/1374497512

Abstract

Let $G$ be a simple algebraic group over $\mathbb{C}$. By taking the quasi-classical limit of the ring of differential operators on the corresponding quantized algebraic group at roots of 1 we obtain a Poisson manifold $\Delta G\times K$, where $\Delta G$ is the subgroup of $G\times G$ consisting of the diagonal elements, and $K$ is a certain subgroup of $G\times G$. We show that this Poisson structure coincides with the one introduced by Semenov-Tyan-Shansky geometrically in the framework of Manin triples.

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Toshiyuki TANISAKI. "Manin Triples and Differential Operators on Quantum Groups." Tokyo J. Math. 36 (1) 49 - 83, June 2013. https://doi.org/10.3836/tjm/1374497512

Information

Published: June 2013
First available in Project Euclid: 22 July 2013

zbMATH: 1301.17015
MathSciNet: MR3112376
Digital Object Identifier: 10.3836/tjm/1374497512

Subjects:
Primary: 20G05
Secondary: 17B37 , 53D99

Rights: Copyright © 2013 Publication Committee for the Tokyo Journal of Mathematics

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Vol.36 • No. 1 • June 2013
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