Reduction of pre-Hamiltonian actions

Antonio De Nicola; Chiara Esposito

doi:10.1016/j.geomphys.2016.03.017

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arXiv · 1507.08821

Reduction of pre-Hamiltonian actions

Antonio De Nicola·Chiara Esposito

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Abstract

We prove a reduction theorem for the tangent bundle of a Poisson manifold $(M, \pi)$ endowed with a pre-Hamiltonian action of a Poisson Lie group $(G, \pi_G)$. 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 $M \times \bar{M}$.

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BibTeX RIS

Antonio De Nicola, Chiara Esposito. 2015-07-31. Reduction of pre-Hamiltonian actions. https://doi.org/10.1016/j.geomphys.2016.03.017

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