Characterization of the absorption radical of an evolution algebra using their associated graph

TL;DR

This paper introduces a graph-based method to identify the absorption radical of finite-dimensional evolution algebras, aiding in understanding their structure and decomposability.

Contribution

It presents a novel approach linking the absorption radical to acyclic vertices in an associated graph, facilitating algebra analysis.

Findings

The method effectively finds the absorption radical using graph theory.

Application to degenerate evolution algebras reveals insights into their decomposability.

The approach simplifies structural analysis of evolution algebras.

Abstract

In this paper we present a method for finding the absorbing radical of a finite-dimensional evolution algebra. Such a method consists of finding the acyclic vertices of an oriented graph associated with the algebra. The set of generators associated with such vertices turn out to be the generators of the absorption radical. As an application we use the absorption radical to study the decomposability of some degenerate evolution algebras.