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 .

DOI Code: 10.1285/i15900932v39n2p71

Keywords: Derivation of Lie algebras; extensions of Lie algebras; second cohomology of Lie algebras; semidirect sum

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