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

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 16 Mar 2007Embargo end date: 01 Jan 2007Publisher:SIGMA (Symmetry, Integrability and Geometry: Methods and Application)Journal:Symmetry, Integrability and Geometry: Methods and Applications (eissn: 1815-0659,

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Authors: Iglesias, D.; Marrero, J.C.; Mart??n de Diego, D.; Mart??nez, E.; Padr??n, E.;

doi: 10.3842/sigma.2007.049 , 10.48550/arxiv.math/0703189

arXiv: math/0703189

handle: 10261/2279

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

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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.

This is a contribution to the Proc. of workshop on Geometric Aspects of Integrable Systems (July 17-19, 2006; Coimbra, Portugal), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

Related Organizations

University of La Laguna
Spain
Spanish National Research Council
Spain
Universidad de La Laguna (ULL)
Spain
Instituto de Física Fundamental
Spain
Universidad de Zaragoza (UNIZAR)/INA
Spain

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Keywords

Mathematics - Differential Geometry, reduction procedure, Lie algebroids and subalgebroids, Symplectic Lie algebroids, 70H05, FOS: Physical sciences, 53D20, Mathematical Physics (math-ph), 58F05, Hamiltonian dynamics, symplectic Lie algebroids, Reduction procedure, Differential Geometry (math.DG), 53D20; 58F05; 70H05, Momentum maps; symplectic reduction, QA1-939, FOS: Mathematics, Mathematics, Mathematical Physics

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