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Non-antisymmetric versions of Nambu-Poisson and Lie algebroids

J. Grabowski·G. Marmo
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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.

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J. Grabowski, G. Marmo. 2001-04-11. Non-antisymmetric versions of Nambu-Poisson and Lie algebroids. https://doi.org/10.1088/0305-4470%2F34%2F18%2F308

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