Non-abelian extensions and automorphisms of post-Lie algebras

Lisi Bai; Tao Zhang

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arXiv · 2409.16289

Non-abelian extensions and automorphisms of post-Lie algebras

Lisi Bai·Tao Zhang

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Abstract

In this paper, we introduce the concepts of crossed modules of post-Lie algebras and cat$^1$-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.

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Lisi Bai, Tao Zhang. 2024-08-29. Non-abelian extensions and automorphisms of post-Lie algebras. https://arxiv.org/abs/2409.16289

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