On Lie-holomorphs of Leibniz Algebras
(2026) Results in Mathematics — Vol. 81, n° 6 (2026)
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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 bideriva-tions 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, & Mancini, M. (2026). On Lie-holomorphs of Leibniz Algebras. Results in Mathematics, 81(6). https://doi.org/10.1007/s00025-026-02704-6 (Original work published 2026)