THE Z(2)-GRADED SCHOUTEN-NIJENHUIS BRACKET AND GENERALIZED SUPER-POISSON STRUCTURES

The super or Z(2)-graded Schouten-Nijenhuis bracket is introduced. Usi ng it, new generalized super-Poisson structures are found which are gi ven in terms of certain. graded-skew-symmetric contravariant tensors L ambda of even order. The corresponding super ''Jacobi identities'' are expressed by stating that these tensors have a zero super Schouten-Ni jenhuis bracket with themselves [Lambda,Lambda]=0. As a particular cas e, we provide the linear generalized super-Poisson structures which ca n be constructed on the dual spaces of simple superalgebras with a non -degenerate Killing metric. The su(3,1) superalgebra is given as a rep resentative example. (C) 1997 American Institute of Physics.