A Note on Evolution Algebras as Banach Algebras

Abstract

With the objective of considering evolution algebras as Banach algebras, we show in this paper new results on normed evolution algebras obtained after the introduction of an evolution algebras operator, which generalizes the one introduced by Tian. The properties of this operator which let evolution algebras be endowed with a Banach space structure are shown.

A Characterization of Associative Evolution Algebras

“…However, evolution algebras are not associative, in general, which means that some of them are. There is not much information on the latter in the literature, that is the reason for which this article can be considered novel, since it presents a result referring to the associativity of these algebras, which can serve to facilitate the study of more aspects related to this topic in general, and complements the study of other aspects of these algebras that are also rarely discussed, such as hierarchy (see [5]), the fact that they are normed (see [6]), or the links between these algebras and Markov chains (see [7]) or between the same and graphs (see [8][9][10], for instance).…”