Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group

Abstract

We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the generality of the theory.

Keywords

• Lie algebroids and subalgebroids
• symplectic Lie algebroids
• Hamiltonian dynamics
• reduction procedure