Journal of Symplectic Geometry

Volume 14 (2016)

Number 1

Linearization of Poisson Lie group structures

Pages: 227 – 267

DOI: http://dx.doi.org/10.4310/JSG.2016.v14.n1.a9

Authors

Anton Alekseev (Section of Mathematics, University of Geneva, Switzerland)

Eckhard Meinrenken (Department of Mathematics, University of Toronto, Ontario, Canada)

Abstract

We show that for any coboundary Poisson Lie group $G$, the Poisson structure on $G^*$ is linearizable at the group unit. This strengthens a result of Enriquez–Etingof–Marshall, who had established formal linearizability of $G^*$ for quasi-triangular Poisson Lie groups $G$. We also prove linearizability properties for the group multiplication in $G^*$ and for Poisson Lie group morphisms, with similar assumptions.

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Published 24 June 2016