Journal of Lie Theory

no. 2
On Quasi-Poisson Homogeneous Spaces of Quasi-Poisson Lie Groups<!-- Anfang Autor -->
Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 543-554
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.
DOI: 10.5802/jolt.351
Classification: 22E30, 53D17, 17B37
Keywords: Lie bialgebra, (quasi-)Poisson Lie group, (quasi-)Poisson homogeneous space 
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     author = {E. Karolinsky and K. Muzykin},
     title = {On {Quasi-Poisson} {Homogeneous} {Spaces} of {Quasi-Poisson} {Lie} {Groups<!--} {Anfang} {Autor} -->},
     journal = {Journal of Lie Theory},
     pages = {543--554},
     year = {2004},
     volume = {14},
     number = {2},
     doi = {10.5802/jolt.351},
     zbl = {1057.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.351/}
}
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E. Karolinsky; K. Muzykin. On Quasi-Poisson Homogeneous Spaces of Quasi-Poisson Lie Groups. Journal of Lie Theory, Volume 14 (2004) no. 2, pp. 543-554. doi: 10.5802/jolt.351

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