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

## TL;DR

This paper introduces omni n-Lie algebras as linearizations of higher Courant algebroids and explores their nonabelian variants related to Nambu-Poisson manifolds, advancing the understanding of higher geometric structures.

## Contribution

It defines omni n-Lie algebras and nonabelian omni n-Lie algebras, linking them to higher Courant algebroids and Nambu-Poisson structures, respectively.

## Key findings

- Omni n-Lie algebras serve as linearizations of higher Courant algebroids.
- Nonabelian omni n-Lie algebras relate to higher Courant algebroids on Nambu-Poisson manifolds.
- The paper establishes new connections between algebraic and geometric higher structures.

## Abstract

In this paper, we introduce the notion of an omni $n$-Lie algebra and show that they are linearization of higher analogues of standard Courant algebroids. We also introduce the notion of a nonabelian omni $n$-Lie algebra and show that they are linearization of higher analogues of Courant algebroids associated to Nambu-Poisson manifolds.