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2 results on '"evolution algebras"'

1. A historical perspective of Tian’s evolution algebras

Author

Ángel F. Tenorio, Manuel Ceballos, Raúl M. Falcón, Juan Núñez-Valdés, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. Departamento de Geometría y Topología, and Junta de Andalucía

Subjects
Evolution algebras, General Mathematics, Genetic algebras, Perspective (graphical), Historical perspective, Tian, Mathematics, Epistemology
Abstract

Even if it has been less than a decade and a half since Tian introduced his concept of evolution algebras to represent algebraically non-Mendelian rules in Genetics, their study is becoming increasingly widespread mainly due to their applications to many scientific disciplines. In order to facilitate further research on the topic, this paper deals with the past and present research on these kind of algebras, together with the most relevant topics regarding them Junta de Andalucía FQM-016

Published
2021

2. A particular type of non-associative algebras and graph theory

Author

Núñez Valdés, Juan, Silvero Casanova, Marithania, Villar Liñán, María Trinidad, Vasek, Vladimir (Coordinador), Shmaliy, Yuriy S. (Coordinador), Trcek, Denis (Coordinador), Kobayashi, Nobuhiko P. (Coordinador), Choras, Ryszard S. (Coordinador), Klos, Zbigniew (Coordinador), Vasek, Vladimir, Shmaliy, Yuriy S., Trcek, Denis, Kobayashi, Nobuhiko P., Choras, Ryszard S., Klos, Zbigniew, Universidad de Sevilla. Departamento de Geometría y Topología, Universidad de Sevilla. Departamento de álgebra, Universidad de Sevilla. FQM326: Geometría Diferencial y Teoría de Lie, and Universidad de Sevilla. FQM164: Matematica Discreta: Teoría de Grafos y Geometría Computacional

Subjects
Evolution operator, Evolution algebras, Non-associative algebras, Graphicable algebras, Pseudo-graphs, Directed graphs
Abstract

Evolution algebras have many connections with other mathematical fields, like group theory, stochastics processes, dynamical systems and other related ones. The main goal of this paper is to introduce a novel non-usual research on Discrete Mathematics regarding the use of graphs to solve some open problems related to the theory of graphicable algebras, which constitute a subset of those algebras. We show as many our advances in this field as other non solved problems to be tackled in future.

Published
2011

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