Mathematical tools for the future: Graph Theory and graphicable algebras

This study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier papers on algebras in general, regarding the use of graphs to study the particular case of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are particularly...

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Detalles Bibliográficos
Autores: Núñez Valdés, Juan, Silvero Casanova, Marithania, Villar Liñán, María Trinidad
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2013
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/167815
Acceso en línea:https://hdl.handle.net/11441/167815
https://doi.org/10.1016/j.amc.2012.12.004
Access Level:acceso abierto
Palabra clave:Graphicable Algebras
Evolution Algebras
Evolution Operator
Directed Graphs
Pseudo-graphs
Descripción
Sumario:This study constitutes the continuation of innovative research in Discrete Mathematics introduced in earlier papers on algebras in general, regarding the use of graphs to study the particular case of graphicable algebras, which form a subset of evolution algebras. Evolution algebras are particularly interesting since they are intrinsically linked with other mathematical fields, such as group theory, stochastics processes, and dynamical systems, for instance. Our advances in this study are obtained by setting a natural correspondence between evolution algebras and direct graphs, in order to translate the general concepts of graphicable algebras: subalgebra, ideal, centralizer, normalizer…to the language of graphs. These translations will enable advances in the application of these algebras to various branches of Mathematics.