Quasi-Centroids and Quasi-Derivations of low-dimensional Zinbiel algebras

TL;DR

This paper introduces the concepts of quasi-centroids and quasi-derivations for low-dimensional Zinbiel algebras, classifies these structures, and identifies a subclass of quasi-characteristically nilpotent algebras.

Contribution

It defines and analyzes quasi-centroids and quasi-derivations in Zinbiel algebras, expanding the understanding of their structure and classification.

Findings

Classification of quasi-centroids in low-dimensional Zinbiel algebras

Identification of quasi-characteristically nilpotent Zinbiel algebras

Properties of quasi-centroids in Zinbiel algebra context

Abstract

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. This description of quasi-derivations allows us to identify a significant subclass of Zinbiel algebras characterized as quasi-characteristically nilpotent.