Non-antisymmetric versions of Nambu-Poisson and Lie algebroids

Details Non-antisymmetric versions of Nambu-Poisson and Lie algebroids Non-antisymmetric versions of Nambu-Poisson and Lie algebroids

2001-04-11

arxiv.org/abs/math/0104122v1

J. Phys. A: Math. Gen. 34 (2001), 3803-3809.

Mathematics

Differential Geometry

LaTex, 8 pages

Scientific paper

10.1088/0305-4470/34/18/308

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.

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