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Classification and (Quasi)-Centroids of Four-Dimensional Ternary Leibniz Algebras

Ahmed Zahari Abdou Damdji

Abstract

We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid and quasi-centroid and compute their dimensions. These results offer a comprehensive description of the internal symmetries of low-dimensional ternary Leibniz algebras and extend several classical results from the binary Leibniz setting to the ternary case.

Classification and (Quasi)-Centroids of Four-Dimensional Ternary Leibniz Algebras

Abstract

We provide a classification, up to isomorphism, of four-dimensional ternary Leibniz algebras over an algebraically closed field of characteristic zero. For each non-abelian algebra in the classification, we explicitly determine its centroid and quasi-centroid and compute their dimensions. These results offer a comprehensive description of the internal symmetries of low-dimensional ternary Leibniz algebras and extend several classical results from the binary Leibniz setting to the ternary case.
Paper Structure (3 sections, 8 theorems, 34 equations)

This paper contains 3 sections, 8 theorems, 34 equations.

Table of Contents

  1. Introduction
  2. Classifications of ternary Leibniz algebras
  3. Quasi-Centroids of Ternary Leibniz Algebras

Key Result

Theorem 2.1

The isomorphism class of 4-dimensional ternary Leibniz algebras given by the following representatives.

Theorems & Definitions (21)

  • Definition 2.1
  • Theorem 2.1
  • Definition 3.1
  • Proposition 3.1
  • proof
  • Definition 3.2
  • Proposition 3.2
  • proof
  • Definition 3.3
  • Definition 3.4
  • ...and 11 more