Geodesic
The Wells map for abelian extensions of 3-Lie algebras
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1133-1164.

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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.
DOI : 10.21136/CMJ.2019.0098-18
Classification : 16E40, 17A36, 17A42
Keywords: automorphisms of 3-Lie algebras; representations of 3-Lie algebras; abelian extensions; cohomology; free nilpotent 3-Lie algebras 
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     title = {The {Wells} map for abelian extensions of {3-Lie} algebras},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1133--1164},
     publisher = {mathdoc},
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Tan, Youjun; Xu, Senrong. The Wells map for abelian extensions of 3-Lie algebras. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 4, pp. 1133-1164. doi : 10.21136/CMJ.2019.0098-18. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2019.0098-18/

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