A characterization of coboundary Poisson Lie groups and Hopf algebras

1996/02/01 by S. Zakrzewski, Zakrzewski, S.
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9602002

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

arxiv created 1996/07/28 · arxiv updated 2009/11/30

Abstract

We show that a Poisson Lie group (G,π) is coboundary if and only if the natural action of G× 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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