bibkey: hu2026idempotent authors: Xing-Yu Hu; Ran Wen year: 2026 title: “Idempotent-free non-solvable evolution algebras over C” doi: 10.48550/arXiv.2609.25023 url: https://arxiv.org/abs/2609.25023v1 claim: “A three-dimensional evolution algebra has a two-dimensional stable derived term without nonzero idempotents.” strata_touched:

• D5/S3/QuadraticForms/EvolutionAlgebras/BareiRemarkThreeFive license: citation-only triage: anchor

Idempotent-free non-solvable evolution algebras over C

Theorem 2.1 and Corollary 2.2 give an exceptional parameter over fields of characteristic different from two. Zero-algebra direct sums extend ambient dimension without increasing the stable dimension. Proposition 2.8 addresses evolution stable terms. These results are credited literature, not newly claimed.

Verified locator

• DOI: https://doi.org/10.48550/arXiv.2609.25023
• URL: https://arxiv.org/abs/2609.25023v1 (v1 submitted 2026-08-12; abstract, HTML and PDF retrieved 2026-10-04).
• Location: Theorem 2.1 and Corollary 2.2 (the exceptional parameter), the direct-sum remark, Proposition 2.8 and Question 2.11.

Reading and scope

Fresh source retrieval on 2026-10-04 returned HTTP 200. The relevant passages were read for the bounded literature check in #12879. No higher-dimensional minimal idempotent-subspace answer was found in the inspected text. This is not-found-in-searched-scope, not exhaustive absence or a priority claim.