On the category of Lie n-algebroids

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].

29 pages, to appear in Journal of Geometry and Physics

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• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• $Q$-manifolds and Higher Analogs of Lie Algebroids
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