arXiv subjects

Ahmed Zahari Abdou Damdji

Publications and source records attributed to Ahmed Zahari Abdou Damdji.

4 recordsLinked to original sources

arXiv2026

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

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.

math.RA↗

arXiv2026

Splitting of operations for Hom-diassociative and Hom-triassociative Algebras

Hom-quadri dendriform algebras and Hom-six-dendriform agebras are introduced and studied which is a splitting of a Hom-diassociative and Hom-triassociative algebras, respectively. Moreover we explore the connections be tween these categories of Hom-algebras. Finally We elaborate a classification of Hom-quadri-dendriform algebra in low dimensional.

math.RA↗

arXiv2025

Related Hom-rhizaform algebras and Rota-Baxter Operators, Hom-Rhizaform Family Algebras

This paper explores the link between Hom-rhizaform algebras and Rota-Baxter operators. We define a new structure, the Hom-rhizaform family algebra, which is a more general version of the Hom-rhizaform algebra. The main finding is that Rota-Baxter operators can be used to construct new Hom-rhizaform algebras. This work expands the theory of Hom-algebras by showing a new way to apply Rota-Baxter operators. Finally, we establish the classification of these algebras as well as their corresponding cocycle cones.

math.RA↗

arXiv2025

Compatible Pairs of Low-Dimensional Associative Algebras and Their Invariants

A compatible associative algebra is a vector space endowed with two associative multiplication operations that satisfy a natural compatibility condition. In this paper, we investigate and classify compatible pairs of associative algebras of complex dimension less than four. Alongside these classifications, we systematically compute and analyze various algebraic invariants associated with them, including derivations, centroids, automorphism groups, quasi-centroids, Rota-Baxter operators, Nijenhuis operators, averaging operators, Reynolds operators, quasi-derivations, and generalized derivations.

math.RA↗