A characterization of coboundary Poisson Lie groups and Hopf algebras

S. Zakrzewski

A characterization of coboundary Poisson Lie groups and Hopf algebras

q-alg 2008-02-03 v2 Quantum Algebra

Authors: S. Zakrzewski

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.

Keywords

coboundary poisson lie groups hopf algebras poisson action quantum analogue su(n)

Cite

@article{arxiv.q-alg/9602002,
  title  = {A characterization of coboundary Poisson Lie groups and Hopf algebras},
  author = {S. Zakrzewski},
  journal= {arXiv preprint arXiv:q-alg/9602002},
  year   = {2008}
}

Comments

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

A characterization of coboundary Poisson Lie groups and Hopf algebras

Abstract

Keywords

Cite

Comments

Related papers