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Manin pairs and moment maps

Anton Alekseev·Yvette Kosmann-Schwarzbach
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Abstract

A Lie group G in a group pair (D,G), integrating a Lie algebra g in a Manin pair (d,g) has a quasi-Poisson structure. We define the quasi-Poisson actions of such Lie groups G, that generalize the Poisson actions of Poisson Lie groups. We define and study the moment maps for those quasi-Poisson actions which are quasi-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 quasi-hamiltonian spaces.

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Anton Alekseev, Yvette Kosmann-Schwarzbach. 1999-09-29. Manin pairs and moment maps. https://arxiv.org/abs/math/9909176

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