Quasi-ideals of Leibniz algebras

Abstract

A subspace H of a Leibniz algebra L is called a quasi-ideal if for every subspace K of L. It includes ideals and subalgebras of codimension one in L. Quasi-ideals of Lie algebras were classified in two remarkable papers by Amayo. The objective here is to extend those results to the larger class of Leibniz algebras, and to classify those Leibniz algebras in which every subalgebra is a quasi-ideal.