Finite dimensional evolution algebras and (pseudo)digraphs

Abstract

In this paper, we focus on the link between evolution algebras and (pseudo)digraphs. We study some theoretical properties about this association and determine the properties of the (pseudo)digraphs associated with each type of evolution algebras. We also analyze the isomorphism classes for each configuration associated with these algebras providing a new method to classify them, and we compare our results with the current classifications of two-and three-dimensional evolution algebras. In order to complement the theoretical study, we have designed and performed the implementation of an algorithm, which constructs and draws the (pseudo)digraph associated with a given evolution algebra and another procedure to study the solvability of a given evolution algebra.

Oriented CW complexes and finite‐dimensional alternative algebras

“…One of the most important types of non‐associative algebras are evolution algebras. There are several papers dealing with the link between these algebras and graphs 15–18 . In those papers, graphs are used in order to study several properties of their associated evolution algebra.…”

CMMSE: Finite-dimensional flexible algebras and oriented CW complexes

“…One of the most important types of non-associative algebras are evolution algebras. There are several papers dealing with the link between these algebras and graphs [8,10,24,4]. In those papers graphs are used in order to study several properties of their associated evolution algebra.…”

On $\exp(Der(E))$ of nilpotent evolution algebras

“…Evolution algebras found their applications in models of non-Mendelian genetics laws [1,2,15,26]. Moreover, these algebras are tightly connected with group theory, the theory of knots, dynamic systems, Markov processes and graph theory [3][4][5]12]. Evolution algebras allowed introduce useful algebraic techniques and methods into the investigation of some digraphs because such kind of algebras and weighted digraphs can be canonically identified [13,28] However, a full classification of nilpotent evolution algebras is far from its solution.…”