Leibniz algebras with absolute maximal Lie subalgebras

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 $\mathsf{Lie}$-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.