Derivations and Centroids of Four Dimensional Associative Algebras

TL;DR

This paper classifies derivations and centroids of four-dimensional associative algebras, utilizing existing classifications, and identifies those that are characteristically nilpotent, contributing to the structural understanding of these algebras.

Contribution

It provides a detailed description of derivations and centroids for four-dimensional associative algebras and identifies characteristically nilpotent cases, expanding the structural classification.

Findings

Descriptions of derivations and centroids for all four-dimensional associative algebras

Identification of characteristically nilpotent algebras within this class

Enhanced understanding of algebraic structures in low dimensions

Abstract

In this paper, we focus on derivations and centroids of four dimensional associative algebras. Using an existing classification result of low dimensional associative algebras, we describe the derivations and centroids of four dimensional associative algebras. We also identify algebra(s) that belong to the characteristically nilpotent class among the algebras of four dimensional associative algebras.