Abstract
The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions \(0 \to A\hookrightarrow L\buildrel \pi \over\longrightarrow B \to 0\) of 3-Lie algebras to obtain obstruction classes in H1 (B, A) for a pair of automorphisms in Aut(A) × Aut(B) to be inducible from an automorphism of L. Application to free nilpotent 3-Lie algebras is discussed.
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