Letters in Mathematical Physics, 103(10), 1103–1133 · 2013
Abstract
In this paper we introduce poly-Poisson structures as a higher-order extension of Poisson
structures. It is shown that any poly-Poisson structure is endowed with a polysymplectic foliation.
It is also proved that if a Lie group acts polysymplectically on a polysymplectic manifold then,
under certain regularity conditions, the reduced space is a poly-Poisson manifold. In addition, some
interesting examples of poly-Poisson manifolds are discussed.