Classification of $2$-dimensional evolution algebras, their groups of automorphisms and derivation algebras

TL;DR

This paper provides a comprehensive classification of 2-dimensional evolution algebras over algebraically closed fields, detailing their automorphism groups and derivation algebras.

Contribution

It offers a complete classification of 2D evolution algebras and characterizes their automorphism and derivation structures, which was previously unexplored.

Findings

Complete classification of 2D evolution algebras

Descriptions of automorphism groups

Descriptions of derivation algebras

Abstract

In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.