Abstract
In this paper, the structure of higher nonabelian omni-Lie algebroid is studied. The concept of higher nonabelian omni-Lie algebroids on direct sum bundle DE⊕∧nJE is introduced, and its related properties are given. It is concluded that the Pre-Dirac structures of higher nonabelian omni-Lie algebroid and n-Lie algebroid have a one-to-one correspondence. By analyzing the matched pair of Leibniz algebroids, it is concluded that higher nonabelian omni-Lie algebroid DE⊕∧nJE can be regarded as a matched pair of two Leibniz algebroids DE and ∧nJE. From the geometric point of view, higher nonabelian omni-Lie algebroid can be regarded as Weinstein linearization of higher analogue of Courant algebroid associated to Nambu-Poisson manifolds.
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