Generalizes Poisson homogeneous space findings in quasi-Poisson Lie groups, suggesting broader application.
Drinfeld showed that if G is a Poisson Lie group with corresponding Lie bialgebra g, then the isomorphism classes of Poisson homogeneous G -spaces are essentially in a 1-1 correspondence with the G -orbits of Lagrangian subalgebras in g g * .The main goal of this paper is to generalize this result to the quasi-Poisson case.We also study the behavior of quasi-Poisson homogeneous spaces under twisting.Some examples of quasi-Poisson homogeneous spaces and corresponding Lagrangian subalgebras are also provided.
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Karolinsky et al. (2004) studied this question.
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