{
  "abstract": "In this note, we illustrate our recent results regarding structure theory of orthogonal Quantum Matrix algebras \\cite{OP-BMW,OP-reciprocal,OP-ortho} using the simplest nontrivial example: the RTT-algebra associated with the canonical orthogonal R-matrix of type $O(3)$ (see, e.g., \\cite{FRT}). By introducing a suitable linear order on the set of generators, we obtain a set of quadratic relations defining the algebra. Next, we investigate relations among its higher-degree polynomials. As a result, we verify `in components' the Cayley-Hamilton and the reciprocal relations, obtained earlier with the use of the R-matrix techniques. We explicitly calculate the coefficients of the characteristic polynomials of quantum matrices and propose a conjecture regarding the form of the Hilbert-Poincaré series for the RTT-algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37813",
  "author_total": 2,
  "authors": [
    {
      "name": "Oleg Ogievetsky"
    },
    {
      "name": "Pavel Pyatov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22man6k0p17x8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37813",
  "fulltext_url": null,
  "id": "22man6k0p17x8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37813",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37813",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22man6k0p17x8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.37813",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37813"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Characteristic identities for orthogonal quantum matrices: examples",
  "title_text": "Characteristic identities for orthogonal quantum matrices: examples",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/22man6k0p17x8",
  "venue": "arXiv",
  "versions": []
}