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...
| Autores: | , , |
|---|---|
| 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 |
| 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. |
|---|