Classification of three-dimensional Nijenhuis Leibniz algebras

TL;DR

This paper classifies all Nijenhuis operators on the thirteen types of three-dimensional Leibniz algebras over the real numbers, expanding understanding of their algebraic structures.

Contribution

It provides a comprehensive analysis of Nijenhuis operators on all classified three-dimensional Leibniz algebras, a novel extension of existing classifications.

Findings

Complete classification of Nijenhuis operators for each algebra type

Identification of structural properties of Nijenhuis operators

Insights into algebraic deformations and integrability

Abstract

There are thirteen types of three-dimensional Leibniz algebras over the real field $\mathbb{R}$ based on the classification given by S. Ayupov, B. Omirov and I. Rakhimov in [Leibniz algebras: structure and classification. CRC Press, Boca Raton, FL, 2020]. In this paper, we investigate all the Nijenhuis operators on these thirteen types of three-dimensional Leibniz algebras.