Remarks on Nambu-Poisson and Nambu-Jacobi brackets

Abstract

It is shown that Nambu-Poisson and Nambu-Jacobi brackets can be defined inductively: a n-bracket, n>2, is Nambu-Poisson (resp. Nambu-Jacobi) if and only if fixing an argument we get a (n-1)-Nambu-Poisson (resp. Nambu-Jacobi) bracket. As a by-product we get relatively simple proofs of Darboux-type theorems for these structures.

Latex, 13 pages

References in corpus (3)

• The local structure of n-Poisson and n-Jacobi manifolds
• On the generalizations of Poisson structures
• Generalized Jacobi structures

Cited by in corpus (7)

• Leibniz algebroid associated with a Nambu-Poisson structure
• Brackets
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• Construction of completely integrable systems by Poisson mappings
• Duality and modular class of a Nambu-Poisson structure
• A variational principle for volume-preserving dynamics
• Jacobi Structures in ${\mathbb{R}}^3$