1991 | OriginalPaper | Chapter
A Universal Reduction Procedure for Hamiltonian Group Actions
Authors : Judith M. Arms, Richard H. Cushman, Mark J. Gotay
Published in: The Geometry of Hamiltonian Systems
Publisher: Springer US
Included in: Professional Book Archive
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
We give a universal method of inducing a Poisson structure on a singular reduced space from the Poisson structure on the orbit space for the group action. For proper actions we show that this reduced Poisson structure is nondegenerate. Furthermore, in cases where the Marsden-Weinstein reduction is well-defined, the action is proper, and the preimage of a coadjoint orbit under the momentum mapping is closed, we show that universal reduction and Marsden-Weinstein reduction coincide. As an èxample, we explicitly construct the reduced spaces and their Poisson algebras for the spherical pendulum.