Journal of Lie Theory

Non-abelian extensions of Lie triple systems and Wells exact sequences
Sun, Qinxiu1; Guo, Shuangjian2 
1Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, P. R. China
2School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, P. R. China
Journal of Lie Theory, Online first, pp. 1-22

In this paper, we investigate non-abelian extensions and inducibility of pairs of automorphisms of Lie triple systems. First, we introduce non-abelian cohomology groups and classify non-abelian extensions in terms of non-abelian cohomology groups. Next, we characterize non-abelian extensions using Maurer–Cartan elements. Furthermore, we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of Lie triple systems. Finally, we state the previous results under the context of abelian extensions of Lie triple systems.

Received:
Accepted:
DOI: 10.5802/jolt.1431
Classification: 17A30, 17B62, 17B38
Keywords: Lie triple system, non-abelian extension, Maurer–Cartan element, inducibility, Wells exact sequence

Sun, Qinxiu  1 ; Guo, Shuangjian  2

1 Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou, 310023, P. R. China
2 School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, 550025, P. R. China 
Sun, Qinxiu; Guo, Shuangjian. Non-abelian extensions of Lie triple systems and Wells exact sequences. Journal of Lie Theory, Online first, pp. 1-22
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