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

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

2009-10-08

arxiv.org/abs/0910.1538v3

Mathematics

Differential Geometry

Scientific paper

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.

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