Using the Evolution Operator to Classify Evolution Algebras

Abstract

Evolution algebras are currently widely studied due to their importance not only “per se” but also for their many applications to different scientific disciplines, such as Physics or Engineering, for instance. This paper deals with these types of algebras and their applications. A criterion for classifying those satisfying certain conditions is given and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions is also analyzed and constructed.

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].…”

Preface to Numerical and Symbolic Computation: Developments and Applications—2021

“…The article "Using the Evolution Operator to Classify Evolution Algebras" is the next work in this Special Issue and it is authored by Fernández-Ternero et al [6]. In this study, the authors consider evolution algebras, currently widely studied due to their importance for their many applications to different scientific disciplines, and propose a criterion for classifying those satisfying certain conditions and an algorithm to obtain degenerate evolution algebras starting from those of smaller dimensions, which is also analyzed and constructed.…”