## Tokyo Journal of Mathematics

### Manin Triples and Differential Operators on Quantum Groups

Toshiyuki TANISAKI

#### 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.

#### Article information

Source
Tokyo J. Math., Volume 36, Number 1 (2013), 49-83.

Dates
First available in Project Euclid: 22 July 2013

https://projecteuclid.org/euclid.tjm/1374497512

Digital Object Identifier
doi:10.3836/tjm/1374497512

Mathematical Reviews number (MathSciNet)
MR3112376

Zentralblatt MATH identifier
1301.17015

#### Citation

TANISAKI, Toshiyuki. Manin Triples and Differential Operators on Quantum Groups. Tokyo J. Math. 36 (2013), no. 1, 49--83. doi:10.3836/tjm/1374497512. https://projecteuclid.org/euclid.tjm/1374497512

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