Reduction of pre-Hamiltonian actions

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 $M\times \bar{M}$.

18 pages, final version, to appear in Journal of Geometry and Physics

References in corpus (3)

• Tangent Lifts of Poisson and Related Structures
• Reduced dynamics and Lagrangian submanifolds of symplectic manifolds
• An extension of the Marsden-Ratiu reduction for Poisson manifolds

Cited by in corpus (1)

• On the Notion of Noncommutative Submanifold