Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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