Computational Approaches to Derivations and Automorphism Groups of Associative Algebras

TL;DR

This paper investigates the derivations and automorphism groups of low-dimensional associative algebras over complex numbers, utilizing classification results and computational tools to reveal their structural features and symmetries.

Contribution

It provides detailed descriptions of derivations and automorphism groups for 2- to 4-dimensional associative algebras using computational methods.

Findings

Classification of automorphism groups for low-dimensional algebras

Identification of structural symmetries in associative algebras

Use of computational tools to analyze algebraic structures

Abstract

This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with computational tools like Mathematica and Maple, we offer detailed descriptions of the derivations and automorphism groups for these algebras. Our analysis of these groups helps to uncover important structural features and symmetries in low-dimensional associative algebras.