Leibniz algebroid associated with a Nambu-Poisson structure

TL;DR

This paper introduces Leibniz algebroids linked to Nambu-Poisson manifolds, enabling the definition of a modular class that extends the concept from Poisson geometry, thus broadening the theoretical framework.

Contribution

It establishes a canonical Leibniz algebroid associated with Nambu-Poisson manifolds and defines a new modular class within this context.

Findings

Canonical Leibniz algebroid exists for each Nambu-Poisson manifold

Modular class of Nambu-Poisson manifolds is defined via cohomology

Extension of Poisson modular class to Nambu-Poisson structures

Abstract

The notion of Leibniz algebroid is introduced, and it is shown that each Nambu-Poisson manifold has associated a canonical Leibniz algebroid. This fact permits to define the modular class of a Nambu-Poisson manifold as an appropiate cohomology class, extending the well-known modular class of Poisson manifolds.