A Note on n-ary Poisson Brackets

Abstract

A class of n-ary Poisson structures of constant rank is indicated. Then, one proves that the ternary Poisson brackets are exactly those which are defined by a decomposable 3-vector field. The key point is the proof of a lemma which tells that an n-vector $(n\ge 3)$ is decomposable iff all its contractions with up to n-2 covectors are decomposable.

References in corpus (1)

• Deformation Quantization and Nambu Mechanics

Cited by in corpus (3)

• A Survey on Nambu-Poisson Brackets
• Notes on Cohomologies of Ternary Algebras of Associative Type
• Some remarks on the Pluecker relations