Matched pairs of Leibniz algebroids, Nambu-Jacobi structures and modular class

Abstract

The notion of a matched pair of Leibniz algebroids is introduced and it is shown that a Nambu-Jacobi structure of order n, n > 2, over a manifold M defines a matched pair of Leibniz algebroids. As a consequence, one deduces that the vector bundle boolean AND (n-1) (T* M) + boolean AND (n-2) (T*M) --> M is a Leibniz algebroid. Finally, if M is orientable, the modular class of M is defined as a cohomology class of order 1 with respect to this Leibniz algebroid.