Singular Reduction of Poisson Manifolds
Source: Letters in Mathematical Physics, Volume 46, Number 4, December 1998 , pp. 359-372(14)
Abstract:The conditions under which it is possible to reduce a Poisson manifold via a regular foliation have been completely characterized by Marsden and Ratiu. In this Letter we show that this characterization can be generalized in a natural way to the singular case and, as a corollary, we obtain that when the singular distribution is given by the tangent spaces to the orbits created by a Hamiltonian Lie group action, one reproduces the Universal Reduction Procedure of Arms, Cushman, and Gotay.
Document Type: Regular Paper
Affiliations: 1: Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland. e-mail: Juan-Pablo.Ortega@epfl.ch 2: Department of Mathematics, University of California, Santa Cruz, Santa Cruz, CA 95064, USA, and Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH 1015 Lausanne, Switzerland. e-mail: Tudor.Ratiu@epfl.ch
Publication date: December 1998