Higher Lie algebra actions on Lie algebroids

Understand

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.