{
  "abstract": "In this paper, we introduce the crystallization $C(SO_0(2n+1)/SO_0(2n-1))$ of the $C^*$-algebra $C(SO_q(2n+1)/SO_q(2n-1))$. We show that every irreducible representation of $C(SO_0(2n+1)/SO_0(2n-1))$ arises as the limit, as $q \\to 0^+$, of a family of irreducible representations of $C(SO_q(2n+1)/SO_q(2n-1))$. As a consequence, we prove that $C(SO_0(2n+1)/SO_0(2n-1))$ is the universal $C^*$-algebra generated by a finite set of generators and relations. We then construct a chain of unital essential short exact sequences of $C^*$-algebras, enabling us to compute the $K$-groups of $C(SO_0(2n+1)/SO_0(2n-1))$ and determine explicit generators for them. Using the theory of homogeneous $C^*$-extensions, we prove that $C(SO_0(2n+1)/SO_0(2n-1))$ is isomorphic to $C(SO_q(2n+1)/SO_q(2n-1))$ for every $q \\in (0,1)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10377",
  "author_total": 3,
  "authors": [
    {
      "name": "Surajit Biswas"
    },
    {
      "name": "Vinay Deshpande"
    },
    {
      "name": "Bipul Saurabh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9bk1hf0mtt83s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10377",
  "fulltext_url": null,
  "id": "9bk1hf0mtt83s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10377",
  "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.OA"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221013944",
  "pdf_url": "https://arxiv.org/pdf/2610.10377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9bk1hf0mtt83s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10377"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Crystallization of the quantum Stiefel manifolds $SO_q(2n+1)/SO_q(2n-1)$",
  "title_text": "Crystallization of the quantum Stiefel manifolds SO_q(2n+1)/SO_q(2n−1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/9bk1hf0mtt83s",
  "venue": "arXiv",
  "versions": []
}