David Iglesias, Juan Carlos Marrero, David Martín de Diego, Eduardo Martínez, Edith Padrón, “Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group”, SIGMA, 2007, Volume 3,049, 28 pp.

This article is cited in 13 papers

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, 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 Matemáatica Aplicada, Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain

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.

MSC: 53D20; 58F05; 70H05

Received: November 14, 2006; in final form March 6, 2007; Published online March 16, 2007

Language: English

DOI: 10.3842/SIGMA.2007.049