Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, Vol. 69, No. 4, pp. 1133-1164, 2019

The Wells map for abelian extensions of 3-Lie algebras

Youjun Tan, Senrong Xu

Received February 23, 2018. Published online August 7, 2019.

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 $0\rightarrow A\hookrightarrow L\stackrel{\pi }{\rightarrow} B\rightarrow0$ 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.

Keywords: automorphisms of 3-Lie algebras; representations of 3-Lie algebras; abelian extensions; cohomology; free nilpotent 3-Lie algebras

Classification MSC: 16E40, 17A42, 17A36

DOI: 10.21136/CMJ.2019.0098-18

PDF available at: Springer Institute of Mathematics CAS Digital Mathematics Library

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Affiliations: Youjun Tan, Senrong Xu (corresponding author), Mathematical College, Sichuan University, No. 24 South Section 1, Yihuan Road, Chengdu, 610064, P. R. China, e-mail: ytan@scu.edu.cn, senrxu@163.com

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