  During the last thirty years, symplectic or Marsden--Weinstein reduction has
been a major tool in the construction of new symplectic manifolds and in the
study of mechanical systems with symmetry. This procedure has been
traditionally associated to the canonical action of a Lie group on a symplectic
manifold, in the presence of a momentum map. In this note we show that the
symplectic reduction phenomenon has much deeper roots. More specifically, we
will find symplectically reduced spaces purely within the Poisson category
under hypotheses that do not necessarily imply the existence of a momentum map.
On other words, the right category to obtain symplectically reduced spaces is
that of Poisson manifolds acted canonically upon by a Lie group.

Symplectic Geometry;Differential Geometry