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.

A Characterization of Associative Evolution Algebras

“…And with respect to the evolution operator of evolution algebras, there are not too many contributions in the literature. Apart from some last works [22] and [23] by the authors of this paper, [25] can also be consulted. In that last short paper of 6 pages, authors review previous results for discrete-time dynamical systems and evolution algebras of sex linked inheritance and discuss some open problems related to such inheritance.…”

“…Three dimensional real evolution algebras with condition dim(E 2 ) = 1 are analyzed in [20], while in [21] the authors study the case of four dimensional perfect non-simple evolution algebras. Classifications involving properties of the main operator of the algebra are dealt with in [22][23].…”