On Automorphism Groups of Idempotent Evolution Algebras

TL;DR

This paper investigates the automorphism groups of idempotent evolution algebras, demonstrating that any finite group can be realized as such and classifying algebras with specific automorphism groups like symmetric groups.

Contribution

It introduces methods to realize any finite group as an automorphism group of an evolution algebra and classifies certain algebras based on their automorphism groups.

Findings

Any finite group can be realized as an automorphism group of an evolution algebra.

Classification of n-dimensional idempotent evolution algebras with automorphism group isomorphic to S_n.

Identification of algebras with maximal diagonal automorphism subgroups.

Abstract

We study the automorphism group of an idempotent evolution algebra, show that any finite group can be the automorphism group of an evolution algebra, and describe certain evolution algebras with given automorphism groups. In particular, we classify $n$-dimensional idempotent evolution algebras whose automorphism group is isomorphic to the symmetric group $S_n$, and classify idempotent evolution algebras with maximal diagonal automorphism subgroups.