Abstract
A Lie group $G$ in a group pair ($D, G$), integrating the Lie algebra $\mathfrak{g}$ in a Manin pair ($\mathfrak{d,g}$), has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups $G$, and show that they generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are hamiltonian. These moment maps take values in the homogeneous space $D/G$. We prove an analogue of the hamiltonian reduction theorem for quasi-Poisson group actions, and we study the symplectic leaves of the orbit spaces of hamiltonian quasi-Poisson spaces.
Citation
Anton Alekseev. Yvette Kosmann-Schwarzbach. "Manin Pairs and Moment Maps." J. Differential Geom. 56 (1) 133 - 165, September, 2000. https://doi.org/10.4310/jdg/1090347528
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