Leibniz algebras with absolute maximal Lie subalgebras

Abstract

A Lie subalgebra of a given Leibniz algebra is said to be an absolute maximal Lie subalgebra if it has codimension one. In this paper, we study some properties of non-Lie Leibniz algebras containing absolute maximal Lie subalgebras. When the dimension and codimension of their Lie-center are greater than two, we refer to these Leibniz algebras as \(s\)-Leibniz algebras (strong Leibniz algebras). We provide a classification of nilpotent Leibniz \(s\)-algebras of dimension up to five.