Nambu-Poisson manifolds and associated n-ary Lie algebroids

TL;DR

This paper introduces a new n-ary Lie algebroid structure linked to Nambu-Poisson manifolds, demonstrating how Nambu-Poisson brackets arise from differential operators and providing physical examples.

Contribution

It establishes a canonical n-ary Lie algebroid for Nambu-Poisson manifolds and characterizes the differential operators inducing Nambu-Poisson brackets.

Findings

Nambu-Poisson brackets are induced by specific differential operators

A canonical n-ary Lie algebroid associated with Nambu-Poisson manifolds is constructed

Physical examples illustrating the theory are provided

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.