Generalized Poisson structures
  New generalized Poisson structures are introduced by using skew-symmetric contravariant tensors of even order. The corresponding `Jacobi identities' are given by the vanishing of the Schouten-Nijenhuis bracket. As an example, we provide the linear generalized Poisson structures which can be constructed on the dual spaces of simple Lie algebras. 
J. A. de Azcarraga, A. M. Perelomov and J. C. Perez Bueno