A Note on n-ary Poisson Brackets
Peter W. Michor, Izu Vaisman
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≥3) is decomposable iff all its contractions with up to n-2 covectors are decomposable.
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