Higher Lie algebra actions on Lie algebroids

被引：2

作者：

Zambon, Marco ^{[1
,2
]}

Zhu, Chenchang ^{[3
]}

机构：

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] ICMAT CSIC UAM UC3M UCM, Madrid 28049, Spain

[3] Univ Gottingen, Courant Res Ctr Higher Order Struct, Gottingen, Germany

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2013年 / 64卷

关键词：

Lie algebroid; NQ-manifold; Double Lie algebroid; Higher Lie algebra action; Higher Lie group action;

D O I：

10.1016/j.geomphys.2012.11.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a simple instance of action up to homotopy. More precisely, we consider strict actions of DGLAs in degrees - 1 and 0 on degree 1 NQ-manifolds. In a more conventional language this means: strict actions of Lie algebra crossed modules on Lie algebroids. When the action is strict, we show that it integrates to group actions in the categories of Lie algebroids and Lie groupoids (i.e. actions of LA-groups and 2-groups). We perform the integration in the framework of Mackenzie's doubles. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：155 / 173

页数：19

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