Non-abelian cohomology of extensions of Lie algebras as Deligne groupoid

Abstract

In this note we show that the theory of non-abelian extensions of a Lie algebra g by a Lie algebra h can be understood in terms of a differential graded Lie algebra L. More precisely we show that the non-abelian cohomology Hnab2(g,h) is MC(L), the π0 of the Deligne groupoid of L.