Solvable Leibniz algebras with triangular nilradicals

TL;DR

This paper extends the classification of solvable Lie algebras with triangular nilradicals to Leibniz algebras, showing that maximal dimension cases are Lie algebras and classifying low-dimensional cases.

Contribution

It generalizes existing results from Lie algebras to Leibniz algebras and characterizes their structure with triangular nilradicals.

Findings

Matrices of operators are upper triangular

Maximal dimension Leibniz algebras are Lie algebras

Low-dimensional cases are classified

Abstract

In this paper the description of solvable Lie algebras with triangular nilradicals is extended to Leibniz algebras. It is proven that the matrices of the left and right operators on elements of Leibniz algebra have upper triangular forms. We establish that solvable Leibniz algebra of a maximal possible dimension with a given triangular nilradical is a Lie algebra. Furthermore, solvable Leibniz algebras with triangular nilradicals of low dimensions are classified.