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Bonavolontà, Giuseppe; Poncin, Norbert

On the category of Lie \(n\)-algebroids. (English) Zbl 1332.58005

J. Geom. Phys. 73, 70-90 (2013).
Summary: 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 Y. Sheng and C. Zhu [Higher extensions of Lie algebroids and application to Courant algebroids. arxiv:1103.5920].

Cited in 48 Documents

MSC:

58H05 Pseudogroups and differentiable groupoids
18D50 Operads (MSC2010)
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
53D55 Deformation quantization, star products
58A50 Supermanifolds and graded manifolds

Keywords:

Lie \(n\)-algebroids; split NQ-manifolds; morphisms; Chevalley-Eilenberg complex; higher derived brackets; Lie infinity (anti)-algebra
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References:

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