Metadata

bibkey: cabrera2025solenoids
authors: Yolanda Cabrera Casado; Maria Inez Cardoso Goncalves; Daniel Goncalves; Dolores Martin Barquero; Candido Martin Gonzalez; Ivan Ruiz Campos
year: 2025
title: "Solenoids in automorphism groups of evolution algebras"
doi: 10.48550/arXiv.2505.14584
url: https://arxiv.org/abs/2505.14584v1
claim: "Example 3.7 gives the algebraic table e_1 squared equals e_1 and e_(i+1) squared equals e_i, with mixed natural-basis products zero."
strata_touched:
  - D5/S3/QuadraticForms/EvolutionAlgebras/HilbertNaturalBasisNonuniqueness
license: citation-only
triage: anchor

An evolution algebra square table

Example 3.7 has the natural-basis multiplication $e_{1}^{2} = e_{1}$ and $e_{i + 1}^{2} = e_{i}$ for every positive integer i, with $e_{i} e_{j} = 0$ for distinct indices. In particular $e_{1}^{2} = e_{2}^{2}$ . This is an algebraic table; a complete Hilbert realization and a dense-square nonuniqueness assertion require their own analytic and basis arguments.

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DOI: https://doi.org/10.48550/arXiv.2505.14584
URL: https://arxiv.org/abs/2505.14584v1
Text: https://arxiv.org/html/2505.14584v1
Location: Example 3.7.

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An evolution algebra square table

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