On the category of Lie n-algebroids

TL;DR

This paper offers a geometric framework for Lie n-algebroids using higher derived brackets, providing explicit formulas, morphism descriptions, and comparisons with NQ-manifolds, advancing the understanding of their structure.

Contribution

It introduces a geometric description of Lie n-algebroids via brackets and anchors, and addresses morphisms, different bases, and conjectures in the field.

Findings

Geometric description of Lie n-algebroids using higher derived brackets

Explicit formula for the Chevalley-Eilenberg differential

Comparison between Lie n-algebroids and NQ-manifolds

Abstract

Lie n-algebroids and Lie infinity algebroids are usually thought of exclusively in supergeometric or algebraic terms. In this work, we apply the higher derived brackets construction to obtain a geometric description of Lie n-algebroids by means of brackets and anchors. Moreover, we provide a geometric description of morphisms of Lie n-algebroids over different bases, give an explicit formula for the Chevalley-Eilenberg differential of a Lie n-algebroid, compare the categories of Lie n-algebroids and NQ-manifolds, and prove some conjectures of Sheng and Zhu [SZ11].