Deformation of a smooth Deligne-Mumford stack via differential graded   Lie algebra
  For a smooth Deligne-Mumford stack over $\CC$, we define its associated Kodaira-Spencer differential graded Lie algebra and show that the deformation functor of the stack is isomorphic to the deformation functor of the Kodaira-Spencer algebra if the stack is proper over $\CC$. 
Yasunari Nagai, Fumitoshi Sato