Chains in evolution algebras

TL;DR

This paper introduces methods to construct three-dimensional evolution algebras from two-dimensional ones, along with new classification tools like stabilizing indices and moduli sets for isomorphism classes.

Contribution

It presents four constructions for three-dimensional evolution algebras derived from two-dimensional algebras and introduces new invariants for their classification.

Findings

Four constructions for three-dimensional evolution algebras from two-dimensional algebras.

Introduction of annihilator and socle stabilizing indices as classification tools.

Use of moduli sets to describe isomorphism classes.

Abstract

In this work we approach three-dimensional evolution algebras from certain constructions performed on two-dimensional algebras. More precisely, we provide four different constructions producing three-dimensional evolution algebras from two-dimensional algebras. Also we introduce two parameters, the annihilator stabilizing index and the socle stabilizing index, which are useful tools in the classification theory of these algebras. Finally, we use moduli sets as a convenient way to describe isomorphism classes of algebras.