{
  "abstract": "Let $\\mathcal A_q$ be the Kronecker quantum cluster algebra with principal coefficients. We construct an explicit algebra homomorphism from the whole quantum group ${U_{q^{1/2}}}( {\\widehat {\\mathfrak{sl}_2}} )$ to $\\mathcal A_q$, whose images together with either of the two frozen variables generate $\\mathcal A_q$. As an application, we obtain algebra homomorphisms from the split $\\imath$quantum groups of affine $\\widehat {\\mathfrak{sl}}_2$ to $\\mathcal A_q$. Moreover, we explicitly determine the images of the positive and negative real and imaginary root vectors of ${U_{q^{1/2}}}( {\\widehat {\\mathfrak{sl}_2}} )$ in terms of quantum cluster variables.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06256",
  "author_total": 4,
  "authors": [
    {
      "name": "Junyuan Huang"
    },
    {
      "name": "Xueqing Chen"
    },
    {
      "name": "Ming Ding"
    },
    {
      "name": "Fan Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rwzj292jsg7w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06256",
  "fulltext_url": null,
  "id": "8rwzj292jsg7w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06256",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06256",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rwzj292jsg7w.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06256",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06256"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "From the quantum group $U_{q^{1/2}}( {\\widehat {\\mathfrak{sl}}}_2 )$ to the Kronecker quantum cluster algebra",
  "title_text": "From the quantum group U_q^1/2( sl̂_2 ) to the Kronecker quantum cluster algebra",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/8rwzj292jsg7w",
  "venue": "arXiv",
  "versions": []
}