dorsal/arxiv
View SchemaA characterization of coboundary Poisson Lie groups and Hopf algebras
| Authors | S. Zakrzewski |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9602002 |
| URL | https://arxiv.org/abs/q-alg/9602002 |
Abstract
We show that a Poisson Lie group $(G,\pi)$ 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 $\pi _+$). We analyze the same condition in the context of Hopf algebras. Quantum analogue of the $\pi_+$ structure on SU(N) is described in terms of generators and relations as an example.
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"abstract": "We show that a Poisson Lie group $(G,\\pi)$ is coboundary if and only if the\nnatural action of $G\\times G$ on $M=G$ is a Poisson action for an appropriate\nPoisson structure on $M$ (the structure turns out to be the well known $\\pi\n_+$). We analyze the same condition in the context of Hopf algebras. Quantum\nanalogue of the $\\pi_+$ structure on SU(N) is described in terms of generators\nand relations as an example.",
"arxiv_id": "q-alg/9602002",
"authors": [
"S. Zakrzewski"
],
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"q-alg",
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"title": "A characterization of coboundary Poisson Lie groups and Hopf algebras",
"url": "https://arxiv.org/abs/q-alg/9602002"
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