Reduction of Poisson Manifolds

Marsden, J. E. and T. S. Ratiu

Lett. in Math. Phys., 11, 161-170

Abstract:

Reduction in the category of Poisson manifolds is defined and some basic properties are derived. The context is chosen to include the usual theorems on reduction of symplectic manifolds, as well as results such as the Dirac bracket and the redhuction to the Lie-Poisson bracket.