A Lazard correspondence for post-Lie rings and skew braces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909353796173824 |
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| author | Trappeniers, Senne |
| author_facet | Trappeniers, Senne |
| contents | We develop a Lazard correspondence between post-Lie rings and skew braces that satisfy a natural completeness condition. This is done through a thorough study of how the Lazard correspondence behaves on semi-direct sums of Lie rings. In particular, for a prime $p$ and $k<p$, we obtain a correspondence between skew braces of order $p^k$ and left nilpotent post-Lie rings of order $p^k$ on a nilpotent Lie ring. This therefore extends results by Smoktunowicz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Lazard correspondence for post-Lie rings and skew braces Trappeniers, Senne Rings and Algebras Group Theory 20N99, 17D25, 20F40 We develop a Lazard correspondence between post-Lie rings and skew braces that satisfy a natural completeness condition. This is done through a thorough study of how the Lazard correspondence behaves on semi-direct sums of Lie rings. In particular, for a prime $p$ and $k<p$, we obtain a correspondence between skew braces of order $p^k$ and left nilpotent post-Lie rings of order $p^k$ on a nilpotent Lie ring. This therefore extends results by Smoktunowicz. |
| title | A Lazard correspondence for post-Lie rings and skew braces |
| topic | Rings and Algebras Group Theory 20N99, 17D25, 20F40 |
| url | https://arxiv.org/abs/2406.02475 |