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Non-antisymmetric versions of Nambu-Poisson and algebroid brackets. (English) Zbl 1021.53059

Summary: The authors show that they can skip the skew-symmetry assumption in the definition of Nambu-Poisson brackets. In other words, an \(n\)-ary bracket on the algebra of smooth functions which satisfies the Leibniz rule and an \(n\)-ary version of the Jacobi identity must be skew symmetric. A similar result holds for a non-antisymmetric version of Lie algebroids.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
17A32 Leibniz algebras
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