Non-antisymmetric versions of Nambu-Poisson and Lie algebroids
Differential Geometry
2009-11-07 v1 Rings and Algebras
Abstract
We show that one can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, a n-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and a n-ary version of the Jacobi identity must be skew-symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.
Cite
@article{arxiv.math/0104122,
title = {Non-antisymmetric versions of Nambu-Poisson and Lie algebroids},
author = {J. Grabowski and G. Marmo},
journal= {arXiv preprint arXiv:math/0104122},
year = {2009}
}
Comments
LaTex, 8 pages