Evolution algebras whose evolution operator is a homomorphism

Abstract

This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank $n-2$ and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.