On the characterization of the space of derivations in evolution algebras

Autor(es)

Cabrera Casado, Yolanda ^[1] ; Cadavid, Paula ^[2] ; Rodino Montoya, Mary Luz ^[3] ; Rodriguez, Pablo M. ^[4]

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Annali di Matematica Pura ed Applicata; v. 200, n. 2 JUN 2020.
• Citações Web of Science: 1

Resumo

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)

• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 16/11648-0 - Teoremas limite e resultados de transição de fase para modelos de propagação de informação em grafos
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 18/06925-0 - Escola Latino Americana de Matemática 2018
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio Organização - Reunião Científica