Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures

Abstract

This article addresses the problem of developing an extension of the Marsden- Weinstein reduction process to symplectic Lie algebroids, and in particular to the case of the symplectic cover of a fiberwise linear Poisson structure, whose reduction process is the analogue to cotangent bundle reduction in the context of Lie algebroids.

36 pages

References in corpus (4)

• Reduction of Courant algebroids and generalized complex structures
• Lagrangian submanifolds and dynamics on Lie algebroids
• Classical Field theory on Lie algebroids: multisymplectic formalism
• Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group

Cited by in corpus (10)

• Poisson Geometry from a Dirac perspective
• Reduction theory for singular symplectic manifolds and singular forms on moduli spaces
• Pre-symplectic algebroids and their applications
• Dirac geometry and integration of Poisson homogeneous spaces
• Coisotropic submanifolds in $b$-symplectic geometry
• Reduction of pre-Hamiltonian actions
• Nonlinear splittings on fibre bundles
• Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
• Hamiltonian facets of classical gauge theories on $E$-manifolds
• K-theory of affine actions