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arXiv · 2512.19276

On Lie-holomorphs of Leibniz algebras

Gianmarco La Rosa·Manuel Mancini
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Abstract

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 $2$.

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Gianmarco La Rosa, Manuel Mancini. 2025-12-22. On Lie-holomorphs of Leibniz algebras. https://doi.org/10.1007/s00025-026-02704-6

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