Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures

This paper addresses the problem of developing an extension of the Marsden-Weinstein reduction process to symplectic-like Lie algebroids, and in particular to the case of the canonical cover of a fiberwise linear Poisson structure, whose reduction process is the analog to cotangent bundle reduction...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2012-04, Vol.45 (16), p.165201-34
Main Authors: Marrero, Juan Carlos, Padrón, Edith, Rodríguez-Olmos, Miguel
Format: Article
Language:English
Subjects:
Bundling
Exact sciences and technology
Lie algebroids
Lie groups
Mathematical analysis
momentum maps
Physics
Reduction
symplectic Lie algebroids
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Summary:This paper addresses the problem of developing an extension of the Marsden-Weinstein reduction process to symplectic-like Lie algebroids, and in particular to the case of the canonical cover of a fiberwise linear Poisson structure, whose reduction process is the analog to cotangent bundle reduction in the context of Lie algebroids. Dedicated to the memory of Jerrold E Marsden
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8113/45/16/165201