A Note on n-ary Poisson Brackets
Symplectic Geometry
2014-11-18 v1
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 is decomposable iff all its contractions with up to n-2 covectors are decomposable.
Keywords
Cite
@article{arxiv.math/9901117,
title = {A Note on n-ary Poisson Brackets},
author = {Peter W. Michor and Izu Vaisman},
journal= {arXiv preprint arXiv:math/9901117},
year = {2014}
}