The automorphism groups and derivation algebras of two-dimensional algebras

TL;DR

This paper classifies the automorphism groups and derivation algebras of all two-dimensional algebras over algebraically closed fields, providing a comprehensive structural understanding.

Contribution

It offers a complete description of automorphism groups and derivation algebras for all two-dimensional algebras, a previously uncharted classification.

Findings

Explicit automorphism groups for each algebra class

Derivation algebras characterized for all cases

Structural insights into two-dimensional algebra symmetries

Abstract

The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.