Nilpotent evolution algebras over arbitrary fields

TL;DR

This paper investigates the structure of nilpotent evolution algebras over arbitrary fields, proposing a classification method for finite-dimensional cases and explicitly classifying those up to dimension four.

Contribution

It introduces an approach to classify finite-dimensional nilpotent evolution algebras and provides a complete classification for dimensions up to four.

Findings

Classified all nilpotent evolution algebras of dimension up to four

Proposed a new method based on annihilator extensions for classification

Established a framework applicable over arbitrary fields

Abstract

The paper is devoted to the study of annihilator extensions of evolution algebras and suggests an approach to classify finite-dimensional nilpotent evolution algebras. Subsequently nilpotent evolution algebras of dimension up to four are classfied.