{
  "abstract": "We determine the representation type and Schurian finiteness of the Tits algebra of a finite central real hyperplane arrangement over an algebraically closed field. The algebra is representation-finite when the arrangement has at most two hyperplanes, tame when it has three, and wild when it has at least four. Moreover, it is Schurian-finite if and only if the arrangement has at most two hyperplanes. Both classifications hold over algebraically closed fields of arbitrary characteristic. The proof combines Saliola's bound-quiver presentation with explicit module constructions, convex subquivers, essentialization, and deletion. In the $\\mathbb{R}^2$ case, we describe all eleven indecomposable modules for two lines and construct a full exact embedding of modules over a free algebra for at least four lines.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16214",
  "author_total": 1,
  "authors": [
    {
      "name": "Siyuan Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/583e4q5h1gg6d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16214",
  "fulltext_url": null,
  "id": "583e4q5h1gg6d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16214",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221777690",
  "pdf_url": "https://arxiv.org/pdf/2610.16214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/583e4q5h1gg6d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Representation Type and Schurian Finiteness of Tits Algebras",
  "title_text": "Representation Type and Schurian Finiteness of Tits Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/583e4q5h1gg6d",
  "venue": "arXiv",
  "versions": []
}