On the category of Lie -algebroids

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• 作者：Giuseppe Bonavolont¨¤ ; Norbert Poncin
• 关键词：Lie nn-algebroids ; Split NQ-manifolds ; Morphisms ; Chevalley&ndash ; Eilenberg complex ; Higher derived brackets ; Lie infinity (anti)-algebra
• 刊名：Journal of Geometry and Physics
• 出版年：2013
• 出版时间：November, 2013
• 年：2013
• 卷：73
• 期：Complete
• 页码：70-90
• 全文大小：526 K

文摘

Lie -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 -algebroids by means of brackets and anchors. Moreover, we provide a geometric description of morphisms of Lie -algebroids over different bases, give an explicit formula for the Chevalley-Eilenberg differential of a Lie-algebroid, compare the categories of Lie -algebroids and NQ-manifolds, and prove some conjectures of Sheng and Zhu? .