Poly-Poisson structures (Q372947)

In this interesting paper the authors introduce poly-Poisson structures as a higher-order generalization of Poisson structures as well as of polysymplectic structures. As for Poisson manifolds, it is proven that any poly-Poisson manifold is endowed with a polysymplectic foliation. Moreover, if \(G\) is a Lie group which acts polysymplectically on a polysymplectic manifold \(M\), then it is shown that, under certain regularity conditions, the reduced space \(M/G\) is a poly-Poisson manifold. Finally, some interesting examples of poly-Poisson manifolds are discussed.