Dirac structures and Poisson homogeneous spaces
  Poisson homogeneous spaces for Poisson groupoids are classfied in terms of Dirac structures for the corresponding Lie bialgebroids. Applications include Drinfel'd's classification in the case of Poisson groups and a description of leaf spaces of foliations as homogeneous spaces of pair groupoids. 
Z.J. Liu, A. Weinstein and P. Xu