Quasi-centroids and quasi-derivations of low-dimensional Zinbiel algebras

I. Basdouri, J. Lerbet, B. Mosbahi

In this paper, we introduce the concepts of quasi-centroid and quasi-derivation for Zinbiel algebras. Utilizing the classification results of Zinbiel algebras established previously, we describe the quasi-centroids and quasi-derivations of low-dimensional Zinbiel algebras. Additionally, we explore certain properties of quasi-centroids in the context of Zinbiel algebras and employ these properties to classify algebras with so-called small quasi-centroids. The description of quasi-derivations allows us to identify a significant subclass of Zinbiel algebras characterized as quasi-characteristically nilpotent. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 18(2) (2025), pp. 253-268