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Keywords:
automorphisms of 3-Lie algebras; representations of 3-Lie algebras; abelian extensions; cohomology; free nilpotent 3-Lie algebras
automorphisms of 3-Lie algebras; representations of 3-Lie algebras; abelian extensions; cohomology; free nilpotent 3-Lie algebras
Summary:
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 $0\rightarrow A\hookrightarrow L\stackrel {\pi }{\rightarrow } B\rightarrow 0$ of 3-Lie algebras to obtain obstruction classes in $H^1(B,A)$ for a pair of automorphisms in ${\rm Aut}(A)\times {\rm Aut}(B)$ to be inducible from an automorphism of $L$. Application to free nilpotent 3-Lie algebras is discussed.
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