Omni n-Lie algebras and linearization of higher analogues of Courant algebroids

Abstract

In this paper, we introduce the notion of an omni [Formula: see text]-Lie algebra and show that it is the linearization of the higher analogue of the standard Courant algebroid. We also introduce the notion of a nonabelian omni [Formula: see text]-Lie algebra and show that it is the linearization of the higher analogue of the Courant algebroid associated to a Nambu–Poisson manifold.