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The momentum map in Poisson geometry
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 131, Number 5, October 2009
- pp. 1261-1310
- 10.1353/ajm.0.0068
- Article
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Every action on a Poisson manifold by Poisson diffeomorphisms lifts to a Hamiltonian action on its symplectic groupoid which has a canonically defined momentum map. We study various properties of this momentum map as well as its use in reduction.