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 ⋀ n−1( T ∗M)⊕⋀ 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.