Derivations of abelian Lie algebra extensions

Abstract

Let $ 0 \rightarrow A\rightarrow L {\rightarrow} B \rightarrow 0 $ be an abelian extension of Lie algebras. In this paper, we construct certain exact sequences which relate derivations with the Lie algebra cohomology group $ H^{2}(B,A) $, and apply them to study extending derivations of $ A $ and lifting derivations of $ B $ to certain derivations of $ L $.