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Journal of Lie Theory 14 (2004), No. 2, 543--554
Copyright Heldermann Verlag 2004
On Quasi-Poisson Homogeneous Spaces of Quasi-Poisson Lie Groups
Eugene Karolinsky
Dept. of Mathematics, Kharkov National University, 4 Svobody Square, Kharkov 61077, Ukraine,
eugene.a.karolinsky@univer.kharkov.ua
Kolya Muzykin
Dept. of Mathematics, Kharkov National University, 4 Svobody Square, Kharkov 61077, Ukraine
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 Å 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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