Motivated by the search for Lie group structures on groups of Poisson diffeomorphisms, we investigate linearizability of the Poisson structure of a Poisson groupoid around the unit section, and present some results in that direction.
Our approach revolves around 'lifting' symplectic- and Poisson geometry to Lie algebroids: we will encounter an algebroid version of Weinstein's Lagrangian neighborhood theorem, and the integration of an algebroid-Poisson structure to an algebroid-symplectic groupoid.
