Artículo
Dealing with the Resolubility of Evolution Algebras
Autor/es | Fernández Ternero, Desamparados
Gómez Sousa, Víctor Manuel Núñez Valdés, Juan |
Departamento | Universidad de Sevilla. Departamento de Geometría y Topología |
Fecha de publicación | 2022 |
Fecha de depósito | 2022-07-04 |
Publicado en |
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Resumen | Although since their introduction by Tian in 2004, evolution algebras have been the subject of a very
deep study in the last years due to their numerous applications to other disciplines, this study is not easy since
these ... Although since their introduction by Tian in 2004, evolution algebras have been the subject of a very deep study in the last years due to their numerous applications to other disciplines, this study is not easy since these algebras lack an identity that characterizes them, such as the identity of Jacobi, for Lie algebras or those of Leibniz and Malcev for those corresponding algebras. In this paper we deal with the concepts of solvability and nilpotency of these evolution algebras. Some novel results on them obtained from using the evolution operator of these algebras are given and some examples illustrating these results are also shown. The main result obtained states that an evolution algebra is solvable if and only if its structure matrix is nilpotent, which implies, in turn, that the solvability and the nilpotency indices of that algebra coincide provided the corresponding evolution operator is an endomorphism of the algebra. |
Cita | Fernández Ternero, D., Gómez Sousa, V.M. y Núñez Valdés, J. (2022). Dealing with the Resolubility of Evolution Algebras. Mathematics in Computer Science, 16, 2-8. |
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