{
  "abstract": "We study the quantized $K$-theoretic Coulomb branches of framed star-shaped quivers with central gauge dimension $n\\geq2$, $r-1$ one-dimensional outer gauge vertices, and a one-dimensional framing at the central vertex. For $n=2$ and arbitrary $r\\geq1$, and for every $n\\geq2$ with $1\\leq r\\leq5$, we prove that the loop-graded Koszul-perverse heart is a monoidal categorification of the associated quantum cluster algebra over $\\mathbb{Z}[v^{\\pm1}]$. This quantum cluster algebra coincides with its upper quantum cluster algebra. For all $n\\geq2$ and $r\\geq1$, we construct an explicit initial seed and identify the associated upper quantum cluster algebra with the Grothendieck ring of this heart. Every mutation is realized by a short exact sequence, and every quantum cluster monomial is represented by a simple object.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.11427",
  "author_total": 1,
  "authors": [
    {
      "name": "Tianle Liu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67p7k6q6qpfbr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.11427",
  "fulltext_url": null,
  "id": "67p7k6q6qpfbr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.11427",
  "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.AG"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221140456",
  "pdf_url": "https://arxiv.org/pdf/2610.11427",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67p7k6q6qpfbr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.11427",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.11427"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers",
  "title_text": "Categorified Cluster Structures on Coulomb Branches of Certain Star-Shaped Quivers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/67p7k6q6qpfbr",
  "venue": "arXiv",
  "versions": []
}