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A Note on n-ary Poisson Brackets

Peter W. Michor·Izu Vaisman
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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 $(n\geq3)$ is decomposable iff all its contractions with up to n-2 covectors are decomposable.

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Peter W. Michor, Izu Vaisman. 1999-01-26. A Note on n-ary Poisson Brackets. https://arxiv.org/abs/math/9901117

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