Regular evolution algebras are closed under subalgebras

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2025_comptes_ladra_regular.pdf (377.75 KB)
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URI: https://hdl.handle.net/10347/47155
E-ISSN: 1778-3569
DOI: 10.48550/arXiv.2503.07187

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2025-11-28

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Académie des Sciences
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Abstract

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.

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Evolution algebras| Regular evolution algebras| Subalgebras

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Ladra, M., & Pérez-Rodríguez, A. (2025) Regular evolution algebras areclosed undersubalgebras, Comptes Rendus Mathématique, 363, 1461-1465. http://creativecommons.org/licenses/by/4.0/

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This work was partially supported by Agencia Estatal de Investigación (Spain), grants PID2020-115155GB-I00 and PID2024-155502NB-I00 (European FEDER support included , UE) and by Xunta de Galicia through the Competitive Reference Groups (GRC), ED431C 2023/31. The second author was also supported by FPU21/05685 scholarship, Ministerio de Educación y Formación Profesional (Spain).

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This article is licensed under the Creative Commons Attribution 4.0 International License. http://creativecommons.org/licenses/by/4.0/
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Centro de Investigación e Tecnoloxía Matemática de Galicia (CITMAga)