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September, 2000 Manin Pairs and Moment Maps
Anton Alekseev, Yvette Kosmann-Schwarzbach
J. Differential Geom. 56(1): 133-165 (September, 2000). DOI: 10.4310/jdg/1090347528

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.

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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

Information

Published: September, 2000
First available in Project Euclid: 20 July 2004

zbMATH: 1046.53055
MathSciNet: MR1863024
Digital Object Identifier: 10.4310/jdg/1090347528

Rights: Copyright © 2000 Lehigh University

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Vol.56 • No. 1 • September, 2000
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