{
  "abstract": "Given a graph $G$, does it have quantum symmetries, or in other words, is the algebra of the quantum automorphism group non-commutative? In the world of ordinary groups, determining whether a finitely presented group is commutative is undecidable. This is an immediate consequence of the Adian-Rabin theorem, which shows that many natural properties of finitely presented groups are undecidable. In this paper, we prove an Adian-Rabin theorem for quantum automorphism groups of graphs, showing that many natural properties of the quantum automorphism group of a graph (including having quantum symmetries) are undecidable. We also show that it's undecidable to determine if the discrete quantum automorphism group is non-trivial. Our methods are based on solution groups of linear system nonlocal games, and we also prove an Adian-Rabin theorem in this context.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40590",
  "author_total": 2,
  "authors": [
    {
      "name": "Josse van Dobben de Bruyn"
    },
    {
      "name": "William Slofstra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23zkpczww54gg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40590",
  "fulltext_url": null,
  "id": "23zkpczww54gg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40590",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
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      "arxiv",
      "math.OA"
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      "math.QA"
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23zkpczww54gg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40590"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An Adian-Rabin theorem for quantum automorphism groups of graphs",
  "title_text": "An Adian-Rabin theorem for quantum automorphism groups of graphs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/23zkpczww54gg",
  "venue": "arXiv",
  "versions": []
}