# On the linearization of Poisson Lie groups

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Speaker:
Eckhard Meinrenken
Affiliation:
Toronto
Date:
Thu, 2014-02-13 15:00 - 16:00
Location:
MPIM Lecture Hall

If a Poisson structure on a manifold \$M\$ vanishes at a point \$x\$, then its linearization is a Poisson structure on the tangent space \$T_x M\$. The Poisson structure on \$M\$ is called linearizable at \$x\$ if there is a germ of a Poisson diffeomorphism  between \$M\$ and \$T_x M\$. For general Poisson manifolds, the linearizability problem is a classical problem, with deep results due to Weinstein, Conn, Dufour, Crainic-Fernandes, and others. Using a simple Moser argument together with some Dirac geometry, we show linearizibility  for certain Poisson Lie groups. (Joint work with Anton Alekseev)

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