Linearization of the higher analogue of Courant algebroids

Abstract

In this paper, we show that the spaces of sections of the n-th differential operator bundle D n E and the n-th skew-symmetric jet bundle J n E of a vector bundle E are isomorphic to the spaces of linear n-vector fields and linear n-forms on E * respectively. Consequently, the n-omni-Lie algebroid DE ⊕ J n E introduced by Bi-Vitagliago-Zhang can be explained as certain linearization, which we call pseudo-linearization of the higher analogue of Courant algebroids T E * ⊕ ∧ n T * E * . On the other hand, we show that the omni n-Lie algebroid DE ⊕ ∧ n JE can also be explained as certain linearization, which we call Weinstein-linearization of the higher analogue of Courant algebroids T E * ⊕ ∧ n T * E * . We also show that n-Lie algebroids, local n-Lie algebras and Nambu-Jacobi structures can be characterized as integrable subbundles of omni n-Lie algebroids. Contents 1 Introduction