Computational Approaches to Derivations and Automorphism Groups of Associative Algebras

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.