On the linearization of Poisson Lie groups

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)