{
  "abstract": "Gélinas introduced the delooping level of an Artin algebra as a homological invariant that bounds the big finitistic dimension of the opposite algebra. A natural question is whether such invariants are preserved under derived equivalences. Chen recently showed that the finiteness of the classical delooping level and its sub-derived variant is not derived-invariant, but the case of the finer derived delooping level of Guo and Igusa remained open. In this paper, we prove that the finiteness of the derived delooping level is \\emph{degree-shift invariant} under derived equivalences: if two algebras are derived equivalent via a tilting complex of width $k_T$, then finiteness of the $(k+k_T)$-derived delooping level on one side implies finiteness of the $k$-derived delooping level on the other. Consequently, the finiteness of the derived $\\infty$-delooping level is invariant under derived equivalences. Furthermore, we introduce the global derived delooping level and prove that, under a derived equivalence, its $\\infty$-version changes by at most $k_T$. In particular, its finiteness is a derived invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29634",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiaqun Wei"
    },
    {
      "name": "Kaili Wu"
    },
    {
      "name": "Weiqing Cao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/89a3y369kxhbx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29634",
  "fulltext_url": null,
  "id": "89a3y369kxhbx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29634",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204967661",
  "pdf_url": "https://arxiv.org/pdf/2608.29634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/89a3y369kxhbx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29634"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Degree-shifted derived invariance of derived delooping levels",
  "title_text": "Degree-shifted derived invariance of derived delooping levels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/89a3y369kxhbx",
  "venue": "arXiv",
  "versions": []
}