On Lie-holomorphs and biderivations of Leibniz algebras
(2026) International Workshop on Non-Associative Algebras — Location: Bari, Italy (13.April.2026)
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- In this talk, we study the notion of 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 show that a linear endomorphism is a Lie-derivation if and only if it is both a derivation and an anti-derivation. Moreover, we provide a classification of the Lie-holomorph algebras of all low-dimensional non-Lie Leibniz algebras over a field of characteristic different from 2. This is joint work with Gianmarco La Rosa (University of Palermo).
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Mancini, M. (2026, April 12). On Lie-holomorphs and biderivations of Leibniz algebras. International Workshop on Non-Associative Algebras, Bari, Italy. https://doi.org/10.1007/978-3-031-32707-0_8