Dirac structures and Poisson homogeneous spaces. (English) Zbl 0921.58074

The classification of Poisson homogeneous spaces for Poisson groupoids in terms of Dirac structures for the corresponding Lie bialgebroids is the main result of the paper. Here Dirac structures correspond to Poisson structures on the quotient manifold. As an application, a new proof of Drinfel’d’s classification of Poisson homogeneous spaces in the case of Poisson groups is obtained.


58H05 Pseudogroups and differentiable groupoids
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
22A22 Topological groupoids (including differentiable and Lie groupoids)
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C30 Differential geometry of homogeneous manifolds
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