Comptes Rendus
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Regular evolution algebras are closed under subalgebras
[Les algèbres d’évolution régulières sont fermées sous les sous-algèbres]
Manuel Ladra1  ; Andrés Pérez-Rodríguez1 
1 Department of Mathematics & CITMAga, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1461-1465

The main goal of this note is to show that subalgebras of regular evolution algebras are themselves evolution algebras. This allows us to assume, without loss of generality, that every subalgebra in the regular setting has a basis consisting of vectors with disjoint supports. Finally, we use this result to characterise the existence of codimension-one subalgebras in regular evolution algebras.

L’objectif principal de cette note est de montrer que les sous-algèbres des algèbres d’évolution régulières sont elles-mêmes des algèbres d’évolution. Cela nous permettra de supposer, sans perte de généralité, que chaque sous-algèbre dans le cadre régulier a une base constituée de vecteurs à supports disjoints. Finalement, nous utiliserons ce résultat pour caractériser l’existence de sous-algèbres de codimension un dans les algèbres d’évolution régulières.

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DOI : 10.5802/crmath.804
Classification : 17D92, 17A60
Keywords: Evolution algebras, regular evolution algebras, subalgebras
Mots-clés : Algèbres d’évolution, algèbres d’évolution régulières, sous-algèbres

Manuel Ladra 1 ; Andrés Pérez-Rodríguez 1

1 Department of Mathematics & CITMAga, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Regular evolution algebras are closed under subalgebras},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1461--1465},
     year = {2025},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {363},
     doi = {10.5802/crmath.804},
     language = {en},
}
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Manuel Ladra; Andrés Pérez-Rodríguez. Regular evolution algebras are closed under subalgebras. Comptes Rendus. Mathématique, Volume 363 (2025), pp. 1461-1465. doi: 10.5802/crmath.804

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