{
  "abstract": "We introduce \\emph{expander evolution algebras} (EEAs), a class of nonassociative algebras defined over an arbitrary field $\\K$ in which the underlying undirected loopless graph of the algebra -- in the sense of Kowalski -- is an expander graph in the classical sense of Cheeger. Starting from the formal graph definition of Kowalski and the algebraic framework of Tian, we establish a dictionary between combinatorial expansion and algebraic structure: the Cheeger constant of the associated graph governs connectivity, the subalgebra lattice, the growth of the evolution sequence, and -- over $\\R$ and $\\C$ -- the spectral gap of the evolution operator. Over a general field $\\K$ we prove that EEAs are always connected and simple (as evolution algebras), carry no proper large evolution subalgebras, and that every generator of a \\emph{symmetric} EEA is algebraically persistent. Over $\\C$ we obtain the sharp Alon--Boppana lower bound for the second eigenvalue of the evolution operator, leading to the definition of \\emph{Ramanujan evolution algebras} as optimal expanders. We also construct families of EEAs from Cayley graphs of finite groups. We close with open problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.12672",
  "author_total": 1,
  "authors": [
    {
      "name": "Piero Giacomelli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5hg00yn53j485.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.12672",
  "fulltext_url": null,
  "id": "5hg00yn53j485",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.12672",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7161145601",
  "pdf_url": "https://arxiv.org/pdf/2605.12672",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5hg00yn53j485.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2605.12672",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.12672"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Expander Evolution Algebras",
  "title_text": "Expander Evolution Algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/5hg00yn53j485",
  "venue": "arXiv",
  "versions": []
}