A note on complete evolution algebras
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Abstract
This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras.
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García-Martínez, X., & Pérez-Rodríguez, A. (2026) A note on complete evolution algebras, Archiv der Mathematik. https://doi.org/10.1007/s00013-026-02251-0
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https://doi.org/10.1007/s00013-026-02251-0Sponsors
Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.
Supported by the projects PID2020-115155GB-I00 and PID2024-155502NB-I00 granted by MICIU/AEI/10.13039/501100011033; and by Xunta de Galicia through the Competitive Reference Groups (GRC), ED431C 2023/31. The second author was also supported by the predoctoral contract FPU21/05685 from the Ministerio de Ciencia, Innovación y Universidades (Spain).
Supported by the projects PID2020-115155GB-I00 and PID2024-155502NB-I00 granted by MICIU/AEI/10.13039/501100011033; and by Xunta de Galicia through the Competitive Reference Groups (GRC), ED431C 2023/31. The second author was also supported by the predoctoral contract FPU21/05685 from the Ministerio de Ciencia, Innovación y Universidades (Spain).
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Attribution 4.0 International
Attribution 4.0 International