Classification of four dimensional perfect non-simple evolution algebras

TL;DR

This paper provides a classification of four-dimensional perfect non-simple evolution algebras over specific fields, considering roots of orders 2, 3, and 7, advancing understanding of their algebraic structure.

Contribution

It offers a complete classification of these algebras under particular field characteristics and root conditions, which was previously unaddressed.

Findings

Classification results for four-dimensional perfect non-simple evolution algebras

Identification of algebraic structures with roots of orders 2, 3, and 7

Enhanced understanding of evolution algebra properties in specified fields

Abstract

We classify the four dimensional perfect non-simple evolution algebras over a field having characteristic different from 2 and in which there are roots of orders 2, 3 and 7.