{
  "abstract": "We prove, under some assumptions, the uniqueness of universal quantum dimension formulae. We first show that the quantum dimensions of classical algebras have a specific form that can be represented universally, in Vogel's sense, as the product/ratio of q-dimension factors with arguments $aα+bβ+cγ$ where $c=0, 1, 2$ and $a, b$ are integers. On this basis, we derive simple uniqueness criteria, according to which all known universal quantum dimensions are unique.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30012",
  "author_total": 2,
  "authors": [
    {
      "name": "M. Y. Avetisyan"
    },
    {
      "name": "R. L. Mkrtchyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8yjgnc7fmwdh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30012",
  "fulltext_url": null,
  "id": "d8yjgnc7fmwdh",
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  "landing_url": "https://arxiv.org/abs/2608.30012",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204964070",
  "pdf_url": "https://arxiv.org/pdf/2608.30012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8yjgnc7fmwdh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.30012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Uniqueness of universal quantum dimensions",
  "title_text": "Uniqueness of universal quantum dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/d8yjgnc7fmwdh",
  "venue": "arXiv",
  "versions": []
}