{
  "abstract": "We show that rigid modules are $τ$-locally free for a large family of 1-Iwanaga--Gorenstein algebras. This family includes many cases of the algebras introduced by Geiss--Leclerc--Schröer in their Inventiones paper \"Quivers with relations for symmetrizable Cartan matrices I: Foundations\", hence answering a question posed by Geiss--Leclerc--Schröer for many new cases. Our result is achieved by introducing coactions of Taft algebras and applying the recent theory developed by the first-named author and Coulembier.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30543",
  "author_total": 2,
  "authors": [
    {
      "name": "Edmund Heng"
    },
    {
      "name": "Calvin Pfeifer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6w4h0yhhsz0r6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30543",
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  "id": "6w4h0yhhsz0r6",
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  "landing_url": "https://arxiv.org/abs/2610.30543",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
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    [
      "arxiv",
      "math.RT"
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    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
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  "openalex": "W7223279019",
  "pdf_url": "https://arxiv.org/pdf/2610.30543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6w4h0yhhsz0r6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30543"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Rigid and $τ$-locally free modules via Taft algebras",
  "title_text": "Rigid and τ-locally free modules via Taft algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/6w4h0yhhsz0r6",
  "venue": "arXiv",
  "versions": []
}