Deformation of infinite dimensional differential graded Lie algebras
  We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.   For elliptic differential graded algebra we construct a complete set of deformations.   We show that for several deformation problems the existence of a formal power series solution guarantees the existence of an analytic solution. 
Maxim Braverman