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

TL;DR

This paper develops a reduction method for symplectic Lie algebroids using Lie subalgebroids and symmetry groups, leading to simplified Hamiltonian dynamics with illustrative examples.

Contribution

It introduces a novel reduction procedure for symplectic Lie algebroids incorporating Lie subalgebroids and symmetry groups, expanding the theoretical framework.

Findings

Reduction procedure for symplectic Lie algebroids established

Reduced Hamiltonian dynamics derived from invariant Hamiltonian functions

Multiple examples demonstrating the theory's applicability

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.