Higher Lie algebra actions on Lie algebroids

Abstract

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.

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

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Cited by in corpus (5)

• A supergeometric approach to Poisson reduction
• L-infinity algebra actions
• Double Groupoids, Orbifolds, and the Symplectic Category
• $L_{\infty }$-actions of Lie algebroids
• Stability of fixed points in Poisson geometry and higher Lie theory