Non-abelian extensions and automorphisms of post-Lie algebras

2024/08/29 by Li Bai, Tao Zhang, Bai, Lisi +1
Mathematics · #17B40 #17B56 #18G45 #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2409.16289

openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the concepts of crossed modules of post-Lie algebras and cat¹-post-Lie algebras. It is proved that these two concepts are equivalent to each other. Secondly, we construct a non-abelian cohomology for post-Lie algebras to classify their non-abelian extensions. At last, we investigate the inducibility problem of a pair of automorphisms for post-Lie algebras and construct a Wells exact sequence to solve it.

Related

• Non-Abelian Cohomology and Extensions of Lie Algebras
• Abelian extensions and crossed modules of Hom-Lie algebras
• Post-Lie algebra structures for perfect Lie algebras
• Crossed modules, non-abelian extensions of associative conformal algebras and Wells exact sequences
• Non-abelian extensions of topological Lie algebras