A characterization of coboundary Poisson Lie groups and Hopf algebras

Stanisław Zakrzewski

ArticleOriginal scientific text

Title

A characterization of coboundary Poisson Lie groups and Hopf algebras

Authors ¹

Affiliations

Department of Mathematical Methods in Physics, University of Warsaw, Hoża 74, 00-682 Warszawa, Poland

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. A quantum analogue of the

π_{+}

structure on SU(N) is described in terms of generators and relations as an example.

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Title

A characterization of coboundary Poisson Lie groups and Hopf algebras

Affiliations

Abstract

Bibliography