On some solvable Leibniz algebras and their completeness

TL;DR

This paper investigates a specific class of solvable Leibniz algebras with particular nilradical properties, providing classifications, uniqueness results, and demonstrating their completeness, thus extending previous findings in the field.

Contribution

It offers a comprehensive classification of solvable Leibniz algebras with certain nilradical conditions, including non-split and split cases, and proves their completeness and uniqueness.

Findings

Classification of solvable Leibniz algebras with specified nilradical properties

Uniqueness of the solvable extensions in this class

Proof of completeness for these Leibniz algebras

Abstract

The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case. Then the case of split nilradical is worked out. We show that the results obtained earlier on this class of Leibniz algebras come as particular cases of the results of this paper. It is shown that such a solvable extension is unique. Finally, we prove that the solvable Leibniz algebras considered are complete.