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.
Citation
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
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