Remarks on Nambu-Poisson and Nambu-Jacobi brackets

摘要

We show that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: an n-bracket, n > 2, is Nambu-Poisson (respectively, Nambu-Jacobi) if and only if on fixing an argument we obtain an (n-1)-Nambu-Poisson (respectively, Nambu-Jacobi) bracket. As a byproduct we obtain relatively simple proofs of Darboux-type theorems for these structures.