Computational Methods for Rota-type operators on 4-dimensionnal nilpotent Leibniz Algebras
Ahmed Zahari Abdou, Kol Béatrice Gamou, Ibrahima Bakayoko
TL;DR
The paper addresses the problem of classifying 4-dimensional complex nilpotent Leibniz algebras and determining their Rota-type operators. It adopts a computational approach, deriving basis-coordinate formulations for Rota-Baxter, Nenjenhuis, Reynolds, and Averaging operators, and provides explicit operator descriptions across the 4D algebra list. The main contributions are the coordinate classifications of these operators on all 4D nilpotent Leibniz algebras and the identification of compatible 4D Leibniz algebra pairs, aided by Mathematica-based computations. This work advances practical computation in the study of low-dimensional Leibniz algebras and their operator theoretic structures, with potential applications in algebraic structure theory and related areas of mathematical physics.
Abstract
A compatible nilpotent Leibniz algebra is a vector space equipped with two multiplication structures that interact in a certain natural way. This article presents the classification of these algebras with dimensions less than four, as well as the classifications of their corresponding Rota-type operators.