Classification and (Quasi)-Centroids of Four-Dimensional Ternary Leibniz Algebras
Rings and Algebras
2026-02-26 v1
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.
Cite
@article{arxiv.2602.21209,
title = {Classification and (Quasi)-Centroids of Four-Dimensional Ternary Leibniz Algebras},
author = {Ahmed Zahari Abdou Damdji},
journal= {arXiv preprint arXiv:2602.21209},
year = {2026}
}