Jotz, Madeleine
Dirac Lie Groups, Dirac Homogeneous Spaces and the Theorem of Drinfeld
Indiana University Mathematics Journal
0022-2518
60
319-366
The notions of Poisson Lie group and Poisson homogeneous space are extended to the Dirac category. The theorem of Drinfeld on the one-to-one correspondence between Poisson homogeneous spaces of a Poisson Lie group and a special class of Lagrangian subalgebras of the Lie bialgebra associated to the Poisson Lie group is proved to hold in this more general setting.
Poisson Lie groups;
Dirac manifolds;
Lie algebras;
Dressing Transformations;
Poisson Groupoids;
Reduction;
Systems;
2011