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.