Higher Lie algebra actions on Lie algebroids

Details Higher Lie algebra actions on Lie algebroids Higher Lie algebra actions on Lie algebroids

2010-12-02

arxiv.org/abs/1012.0428v2

Mathematics

Differential Geometry

29 pages. Presentation improved. Sections 1.3 and 4 have been removed (see arXiv:1202.1378)

Scientific paper

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.

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