Nambu-Poisson manifolds and associated n-ary Lie algebroids

Abstract

We introduce an n-ary Lie algebroid canonically associated with a Nambu-Poisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize such operators. Some physical examples are presented.

References in corpus (5)

• Lie algebroids and Poisson-Nijenhuis structures
• Leibniz algebroid associated with a Nambu-Poisson structure
• The local structure of n-Poisson and n-Jacobi manifolds
• On the generalizations of Poisson structures
• Quantization of Poisson algebras associated to Lie algebroids

Cited by in corpus (4)

• Lie algebroids, non-associative structures and non-geometric fluxes
• The infinite dimensional Unital 3-Lie Poisson algebra
• Higher derived brackets, strong homotopy associative algebras and Loday pairs
• Nambu system associated with n-dimensional maps