A characterization of coboundary Poisson Lie groups and Hopf algebras

S. Zakrzewski

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arXiv · q-alg/9602002

A characterization of coboundary Poisson Lie groups and Hopf algebras

S. Zakrzewski

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Abstract

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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BibTeX RIS

S. Zakrzewski. 1996-07-28. A characterization of coboundary Poisson Lie groups and Hopf algebras. https://arxiv.org/abs/q-alg/9602002

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