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

ABSTRACT: 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.

• Autores: Rodiño Montoya, Mary Luz; Cadavid Salazar, Paula Andrea; Rodríguez, Pablo Martín
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2020
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/37286
• Acceso en línea: https://hdl.handle.net/10495/37286
• Palabra clave: Ecuaciones de evolución; Evolution equations; Teoría de grafos; Graph theory; Álgebra; Algebra
• Rights: openAccess
• License: http://creativecommons.org/licenses/by-nc-nd/2.5/co/