SIGMA 3 (2007), 049, 28 pages      math.DG/0703189      https://doi.org/10.3842/SIGMA.2007.049
Contribution to the Proceedings of the Coimbra Workshop on Geometric Aspects of Integrable Systems

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

David Iglesias ^a, Juan Carlos Marrero ^b, David Martín de Diego ^a, Eduardo Martínez ^c and Edith Padrón ^b
a) Departamento de Matemáticas, Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas, Serrano 123, 28006 Madrid, Spain
^b) Departamento de Matemática Fundamental, Facultad de Matemáticas, Universidad de la Laguna, La Laguna, Tenerife, Canary Islands, Spain
^c) Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

Received November 14, 2006, in final form March 06, 2007; Published online March 16, 2007

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.

Key words: Lie algebroids and subalgebroids; symplectic Lie algebroids; Hamiltonian dynamics; reduction procedure.

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