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arXiv q-alg/96020021996-02q-algmath.QA

A characterization of coboundary Poisson Lie groups and Hopf algebras

S. Zakrzewski

备注：: 6 pages, PlainTeX, 2 (minor) typos corrected, to appear in Proceedings of QG&QS, Banach Center in Warsaw, Nov. 1995

英文摘要：

We show that a Poisson Lie group $(G,π)$ is coboundary if and only if the natural action of $G\times G$ on $M=G$ is a Poisson action for an appropriate Poisson structure on $M$ (the structure turns out to be the well known $π_+$). We analyze the same condition in the context of Hopf algebras. Quantum analogue of the $π_+$ structure on SU(N) is described in terms of generators and relations as an example.

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