The Local Structure of N-poisson and N-jacobi Manifolds

@inproceedings{Marmo1997TheLS,
title={The Local Structure of N-poisson and N-jacobi Manifolds},
author={Giuseppe Marmo and G. Vilasi and Alexander M Vinogradov},
year={1997}
}

n-Lie algebra structures on smooth function algebras given by means of multi-differential operators, are studied. Necessary and sufficient conditions for the sum and the wedge product of two n-Poisson sructures to be again a multi-Poisson are found. It is proven that the canonical n-vector on the dual of an n-Lie algebra g is n-Poisson iff dim g ≤ n + 1. The problem of compatibility of two n-Lie algebra structures is analyzed and the compatibility relations connecting hereditary structures of a… CONTINUE READING