Dirac Lie groups, Dirac homogeneous spaces and the Theorem of Drinfeld

The notions of \emph{ Poisson Lie group} and \emph{ Poisson homogeneous space} are extended to the Dirac category. The theorem of Drinfel$'$d (\cite{ Drinfeld93}) 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.

Categories: math.DG