{
  "abstract": "Let $\\Bbbk$ be an algebraically closed field of characteristic different from $2$. We realize the four-dimensional selfinjective algebra $Ω(1)$ as an admissible infinite cyclic orbit algebra of the repetitive Kronecker category. Thus an algebra long stated to be nonstandard is of Euclidean type in the orbit-algebra sense. We also identify a gap in an earlier proof of its nonstandardness and give an independent proof by determining all connected Galois covering sources of $Ω(1)$. Together, these results disprove the implication from Euclidean type to standardness in the equivalence explicitly stated by Bocian--Holm--Skowroński (2004) and Bocian--Skowroński (2005). They also contradict the standardness conclusion of the Proposition in \\S2.1 of Skowroński (1989); its main theorem in \\S1.5 assumes standardness and is not contradicted by this example.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34119",
  "author_total": 1,
  "authors": [
    {
      "name": "Hideto Asashiba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/czsxhvpe758tj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34119",
  "fulltext_url": null,
  "id": "czsxhvpe758tj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34119",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223901619",
  "pdf_url": "https://arxiv.org/pdf/2610.34119",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/czsxhvpe758tj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34119",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34119"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A nonstandard selfinjective algebra of Euclidean type",
  "title_text": "A nonstandard selfinjective algebra of Euclidean type",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/czsxhvpe758tj",
  "venue": "arXiv",
  "versions": []
}