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On the linearization of Poisson Lie groups

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Eckhard Meinrenken
Thu, 2014-02-13 15:00 - 16:00
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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