GENERALIZED JACOBI STRUCTURES

Jacobi brackets (a generalization of standard Poisson brackets in whic h Leibniz's rule is replaced by a weaker condition) are extended to br ackets involving an arbitrary (even) number of functions. This new str ucture includes, as a particular case, the recently introduced general ized Poisson structures. The linear case on simple group manifolds is also studied and non-trivial examples (different from those coming fro m generalized Poisson structures) of this new construction are found b y using the cohomology ring of the given group.