{
  "abstract": "Let $B$ be a finite-dimensional algebra, $M\\in\\modu B$, and $A=B[M]$ the one-point extension. We give a stable two-step extension criterion for the new simple $A$-module to have derived delooping level at most one. For a concrete algebra $B$ with a self-injective Nakayama quotient $R$, we determine the derived and classical delooping levels of $B[M]$ for every nonzero $M\\in\\modu R$. In particular, we obtain an explicit algebra $A$ satisfying \\[ \\Findim(A^{\\mathrm{op}})=1<2=\\ddell A=\\dell A, \\] which gives a negative answer to a question of Guo and Igusa.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32744",
  "author_total": 3,
  "authors": [
    {
      "name": "Hanpeng Gao"
    },
    {
      "name": "Dajun Liu"
    },
    {
      "name": "Ruomu Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cbm84yefev975.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32744",
  "fulltext_url": null,
  "id": "cbm84yefev975",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32744",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214777983",
  "pdf_url": "https://arxiv.org/pdf/2609.32744",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cbm84yefev975.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.32744",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32744"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions",
  "title_text": "Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/cbm84yefev975",
  "venue": "arXiv",
  "versions": []
}