Automorphism groups of Cayley evolution algebras

TL;DR

This paper introduces Cayley evolution algebras and proves that over sufficiently large fields, every finite group can be realized as the automorphism group of such an algebra, expanding understanding of algebraic symmetries.

Contribution

The paper defines Cayley evolution algebras and demonstrates that any finite group can be represented as their automorphism group over large fields.

Findings

Every finite group is isomorphic to the automorphism group of a Cayley evolution algebra over sufficiently large fields.

Cayley evolution algebras are a new class of evolution algebras with rich automorphism structures.

The results connect group theory and algebraic structures through automorphism groups.

Abstract

In this paper we introduce a new species of evolution algebras that we call Cayley evolution algebras. We show that if a field $k$ contains sufficiently many elements (for example if $k$ is infinite) then every finite group $G$ is isomorphic to $Aut(X)$ where $X$ is a finite-dimensional absolutely simple Cayley evolution $k$-algebra.