We prove a reduction theorem for the tangent bundle of a Poisson manifold (M,π) endowed with a pre-Hamiltonian action of a Poisson–Lie group (G,πG). In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden–Ratiu reduction of M. If the manifold M is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden–Weinstein reduction of the pair groupoid M×M̄. © 2016 Elsevier B.V.
Reduction of pre-Hamiltonian actions
DE NICOLA, Antonio;ESPOSITO, Chiara
2017
Abstract
We prove a reduction theorem for the tangent bundle of a Poisson manifold (M,π) endowed with a pre-Hamiltonian action of a Poisson–Lie group (G,πG). In the special case of a Hamiltonian action of a Lie group, we are able to compare our reduction to the classical Marsden–Ratiu reduction of M. If the manifold M is symplectic and simply connected, the reduced tangent bundle is integrable and its integral symplectic groupoid is the Marsden–Weinstein reduction of the pair groupoid M×M̄. © 2016 Elsevier B.V.File in questo prodotto:
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