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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On the characterization of the space of derivations in evolution algebras

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Author(s):
Cabrera Casado, Yolanda [1] ; Cadavid, Paula [2] ; Rodino Montoya, Mary Luz [3] ; Rodriguez, Pablo M. [4]
Total Authors: 4
Affiliation:
[1] Univ Malaga, Dept Matemat Aplicada, Campus Teatinos S-N, Malaga 29071 - Spain
[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, Ave Estados 5001, Santo Andre, SP - Brazil
[3] Univ Antioquia, Inst Matemat, Calle 67, Medellin 53108 - Colombia
[4] Univ Fed Pernambuco, Ctr Ciencias Exatas & Nat, Av Prof Moraes Rego 1235, Cidade Univ, Recife, PE - Brazil
Total Affiliations: 4
Document type: Journal article
Source: Annali di Matematica Pura ed Applicata; v. 200, n. 2 JUN 2020.
Web of Science Citations: 1
Abstract

We study the space of derivations for some finite-dimensional evolution algebras, depending on the twin partition of an associated directed graph. For evolution algebras with a twin-free associated graph, we prove that the space of derivations is zero. For the remaining families of evolution algebras, we obtain sufficient conditions under which the study of such a space can be simplified. We accomplish this task by identifying the null entries of the respective derivation matrix. Our results suggest how strongly the associated graph's structure impacts in the characterization of derivations for a given evolution algebra. Therefore, our approach constitutes an alternative to the recent developments in the research of this subject. As an illustration of the applicability of our results, we provide some examples and we exhibit the classification of the derivations for non-degenerate irreducible three-dimensional evolution algebras. (AU)

FAPESP's process: 17/10555-0 - Stochastic modeling of interacting systems
Grantee:Fabio Prates Machado
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 16/11648-0 - Limit theorems and phase transition results for information propagation models on graphs
Grantee:Pablo Martin Rodriguez
Support Opportunities: Regular Research Grants
FAPESP's process: 18/06925-0 - 2018 Latin American School of Mathematics
Grantee:Pablo Martin Rodriguez
Support Opportunities: Organization Grants - Scientific Meeting