Jacobson identities for post-Lie algebras in positive characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912815754772480 |
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| author | Ehret, Quentin Gilliers, Nicolas |
| author_facet | Ehret, Quentin Gilliers, Nicolas |
| contents | Let $p$ be a prime number. Given a restricted Lie algebra over a field of characteristic $p$ and a post-Lie operation over it, we prove the Jacobson identities for a $p$-structure built from the Lie bracket and the post-Lie operation, called sub-adjacent $p$-structure. Furthermore, we give sufficient conditions for the sub-adjacent Lie algebra to be restricted if equipped with this sub-adjacent $p$-structure. This construction is ''axiomatized'' by introducing the notion of restricted post-Lie algebras, and we work out several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14540 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jacobson identities for post-Lie algebras in positive characteristic Ehret, Quentin Gilliers, Nicolas Rings and Algebras 17B50, 17B60 Let $p$ be a prime number. Given a restricted Lie algebra over a field of characteristic $p$ and a post-Lie operation over it, we prove the Jacobson identities for a $p$-structure built from the Lie bracket and the post-Lie operation, called sub-adjacent $p$-structure. Furthermore, we give sufficient conditions for the sub-adjacent Lie algebra to be restricted if equipped with this sub-adjacent $p$-structure. This construction is ''axiomatized'' by introducing the notion of restricted post-Lie algebras, and we work out several examples. |
| title | Jacobson identities for post-Lie algebras in positive characteristic |
| topic | Rings and Algebras 17B50, 17B60 |
| url | https://arxiv.org/abs/2504.14540 |