Lectures on Poisson groupoids

Abstract

In these lecture notes, we give a quick account of the theory of Poisson groupoids and Lie bialgebroids. In particular, we discuss the universal lifting theorem and its applications including integration of quasi-Lie bialgebroids, integration of Poisson Nijenhuis structures and Alekseev and Kosmann-Schwarzbach's theory of D/G-momentum maps.

27 pages, notes of lectures given by the third author at the summer school on Poisson geometry held at I.C.T.P. Trieste in July 2005