Non-abelian extensions of Lie triple systems and Wells exact sequences
Rings and Algebras
2024-06-24 v1
Abstract
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 the non-abelian extensions in terms of non-abelian cohomology groups. Next, we characterize the 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.
Keywords
Cite
@article{arxiv.2406.14577,
title = {Non-abelian extensions of Lie triple systems and Wells exact sequences},
author = {Qinxiu Sun and Shuangjian Guo},
journal= {arXiv preprint arXiv:2406.14577},
year = {2024}
}
Comments
23 pages. arXiv admin note: substantial text overlap with arXiv:2401.15333, arXiv:2404.02752