On Lie-holomorphs and biderivations of Leibniz algebras

Abstract

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).