On a class of two-step solvable Leibniz algebras

Abstract

This paper studies a class of solvable Leibniz algebras, which is a generalisation of Lie algebras. Specifically, we examine 2-step solvable Leibniz algebras that possess a 2-dimensional abelian derived subalgebra. Leveraging previous findings, we explore the left action vector spaces and establish a lower bound on the dimension of the algebra's center in order to classify such indecomposable solvable Leibniz algebras. The main result states that such a Leibniz algebra either has a dimension at most 7 or is described by a bilinear form.