An Extension of the Marsden–Ratiu Reduction for Poisson Manifolds

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are...

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Bibliographic Details
Published in:Letters in mathematical physics 2008-09, Vol.85 (2-3), p.203-219
Main Authors: Falceto, Fernando, Zambon, Marco
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-008-0262-7