Characterization theorems for the spaces of derivations of evolution algebras associated to graphs

Autor(es)

Cadavid, Paula ^[1] ; Rodino Montoya, Mary Luz ^[2] ; Rodriguez, Pablo M. ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Antioquia, Inst Matemat, Medellin - Colombia

• Tipo de documento: Artigo Científico
• Fonte: LINEAR & MULTILINEAR ALGEBRA; v. 68, n. 7, p. 1340-1354, JUL 2 2020.
• Citações Web of Science: 4

Resumo

It is well-known that the space of derivations of n-dimensional evolution algebras with non-singular matrices is zero. On the other hand, the space of derivations of evolution algebras with matrices of rank n-1 have also been completely described in the literature. In this work, we provide a complete description of the space of derivations of evolution algebras associated to graphs, depending on the twin partition of the graph. For graphs without twin classes with at least three elements, we prove that the space of derivations of the associated evolution algebra is zero. Moreover, we describe the spaces of derivations for evolution algebras associated to the remaining families of finite graphs. It is worth pointing out that our analysis includes examples of finite dimensional evolution algebras with matrices of any rank. (AU)

• 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: 17/19433-5 - 6o Workshop de Métodos Estatísticos e Probabilísticos
• Beneficiário: Pablo Martin Rodriguez
• Modalidade de apoio: Auxílio Organização - Reunião Científica
• Processo FAPESP: 17/10555-0 - Modelagem estocástica de sistemas interagentes
• Beneficiário: Fabio Prates Machado
• Modalidade de apoio: Auxílio à Pesquisa - Temático