Complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras

TL;DR

This paper provides a comprehensive classification of all two-dimensional real algebras across several types, including general, commutative, Jordan, division, and evolution algebras, and details their automorphisms and derivations.

Contribution

It offers the first complete classification of these algebra types in two dimensions, including automorphism and derivation structures for evolution algebras.

Findings

Complete classification of two-dimensional real algebras across multiple types.

Descriptions of automorphism groups and derivation algebras for evolution algebras.

Identification of structural differences among algebra types.

Abstract

A complete classifications of two-dimensional general, commutative, commutative Jordan, division and evolution real algebras are given. In the case of evolution algebras their groups of automorphisms and derivation algebras are described as well.