{
  "abstract": "We study the $2$-representation theory of the Taft category, the tensor category of finite-dimensional modules over the Taft algebra. This category has two left cells. We first classify suitable transitive modules over its based representation ring. For the upper cell, we recall a construction by Etingof and Ostrik giving an infinite family of pairwise nonequivalent simple $2$-representations. For the bottom cell, we pass to the semisimplification of the Taft category and identify a distinguished fusion subcategory with an adjoint $\\mathfrak{sl}_2$ Verlinde category. Using algebra objects associated with $\\mathsf{ADET}$-diagrams and categorical Clifford theory, we classify the regular exact indecomposable module categories of this semisimplification. For these regular module categories, the split Grothendieck group is a complete invariant. Finally, we identify the two cell $2$-representations of the Taft category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28534",
  "author_total": 1,
  "authors": [
    {
      "name": "Raphaël Paegelow"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6j05ftjk011jc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28534",
  "fulltext_url": null,
  "id": "6j05ftjk011jc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28534",
  "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.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223087870",
  "pdf_url": "https://arxiv.org/pdf/2610.28534",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6j05ftjk011jc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28534",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28534"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "2-representation theory of the Taft algebra",
  "title_text": "2-representation theory of the Taft algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/6j05ftjk011jc",
  "venue": "arXiv",
  "versions": []
}