On the property of subalgebras of Evolution algebras

TL;DR

This paper classifies nilpotent complex evolution algebras where all subalgebras are also evolution subalgebras with extendable bases, and proposes conjectures for non-nilpotent cases.

Contribution

It provides a classification of a specific class of nilpotent evolution algebras and introduces conjectures for broader non-nilpotent cases.

Findings

Classified nilpotent evolution algebras with certain subalgebra properties

Identified conditions for subalgebras to be extendable bases

Formulated conjectures for non-nilpotent evolution algebras

Abstract

In this paper we study subalgebras of complex finite dimensional evolution algebras. We obtain the classification of nilpotent evolution algebras whose any subalgebra is an evolution subalgebra with a basis which can be extended to a natural basis of algebra. Moreover, we formulate three conjectures related to description of such non-nilpotent algebras.