Classification in chains of three-dimensional real evolution algebras

TL;DR

This paper classifies three-dimensional real evolution algebras within chains of evolution algebras depending on time, providing explicit functions that generate all such algebras and analyzing their structural properties.

Contribution

It offers a complete classification of three-dimensional real evolution algebras in chains, including explicit functions that generate all possible algebras over time.

Findings

Full classification of three-dimensional real evolution algebras in CEAs

Explicit functions ensuring the inclusion of all possible algebras

Analysis of structural constants satisfying Kolmogorov-Chapman equation

Abstract

A chain of evolution algebras (CEA) is an uncountable family (depending on time) of evolution algebras on the field of real numbers. The matrix of structural constants of a CEA satisfies Kolmogorov-Chapman equation. In this paper, we consider three CEAs of three-dimensional real evolution algebras. These CEAs depend on several (non-zero) functions defined on the set of time. For each chain we give full classification (up to isomorphism) of the algebras depending on the time-parameter. We find concrete functions ensuring that the corresponding CEA contains all possible three-dimensional evolution algebras.