A Note on n-ary Poisson Brackets

Details A Note on n-ary Poisson Brackets A Note on n-ary Poisson Brackets

1999-01-26

arxiv.org/abs/math/9901117v1

Rendiconti del Circolo Matematico di Palermo, Serie II, Suppl. 63 (2000), 165-172

Mathematics

Symplectic Geometry

Scientific paper

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 $(n\geq3)$ is decomposable iff all its contractions with
up to n-2 covectors are decomposable.

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