Non-abelian extensions and automorphisms of post-Lie algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866918219036491776 |
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| author | Bai, Lisi Zhang, Tao |
| author_facet | Bai, Lisi Zhang, Tao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16289 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-abelian extensions and automorphisms of post-Lie algebras Bai, Lisi Zhang, Tao Rings and Algebras 17B40, 17B56, 18G45 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. |
| title | Non-abelian extensions and automorphisms of post-Lie algebras |
| topic | Rings and Algebras 17B40, 17B56, 18G45 |
| url | https://arxiv.org/abs/2409.16289 |