On Lie-holomorphs of Leibniz algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911332263002112 |
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| author | La Rosa, Gianmarco Mancini, Manuel |
| author_facet | La Rosa, Gianmarco Mancini, Manuel |
| contents | We study the notion of the Lie-holomorph of a Leibniz algebra, recently introduced by N. P. Souris as a generalisation of the classical holomorph construction for Lie algebras. We establish a connection between the Lie-holomorph construction and the Leibniz algebra of biderivations defined by J.-L. Loday, and we prove that a linear endomorphism is a Lie-derivation if and only if it is simultaneously a derivation and an anti-derivation. As an application, we classify the Lie-holomorph algebras of all low-dimensional non-Lie Leibniz algebras over a field of characteristic different from $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19276 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Lie-holomorphs of Leibniz algebras La Rosa, Gianmarco Mancini, Manuel Rings and Algebras 15B30, 16W25, 17A32, 17A36, 17B40 We study the notion of the Lie-holomorph of a Leibniz algebra, recently introduced by N. P. Souris as a generalisation of the classical holomorph construction for Lie algebras. We establish a connection between the Lie-holomorph construction and the Leibniz algebra of biderivations defined by J.-L. Loday, and we prove that a linear endomorphism is a Lie-derivation if and only if it is simultaneously a derivation and an anti-derivation. As an application, we classify the Lie-holomorph algebras of all low-dimensional non-Lie Leibniz algebras over a field of characteristic different from $2$. |
| title | On Lie-holomorphs of Leibniz algebras |
| topic | Rings and Algebras 15B30, 16W25, 17A32, 17A36, 17B40 |
| url | https://arxiv.org/abs/2512.19276 |