{
  "annotation_id": "acecc6d9-35e6-4e2f-bb2a-9c486cd73f79",
  "date_created": "2026-02-17T05:53:16.088000Z",
  "date_modified": "2026-02-17T05:53:16.088000Z",
  "file_hash": "154bb1c42cb9ca1fee52d8a9750a82d20a65feb72b3ac1ec602703291139bc59",
  "private": false,
  "record": {
    "abstract": "We study the specializations $\\mathcal{L}_{g,n}^\\epsilon$ at roots of unity $\\epsilon$ of odd order of the graph algebras, associated to a simply-connected complex semi-simple algebraic group $G$ and a compact oriented surface $\\Sigma_{g,n}^{\\circ}$ with genus $g$, $n$ punctures, and one boundary component. We prove that the central localizations of $\\mathcal{L}_{g,n}^\\epsilon$ and of its subalgebra $\\mathcal{L}_{g,n}^{u_\\epsilon}$ of invariant elements under the coadjoint action of a small quantum group, are central simple algebras of PI degrees that we compute. Also, we describe their centers, and show they are integrally closed rings.",
    "arxiv_id": "2601.08789",
    "authors": [
      "St\u00e9phane Baseilhac",
      "Matthieu Faitg",
      "Philippe Roche"
    ],
    "categories": [
      "math.QA",
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On the structure and representations of quantum graph algebras at roots of unity",
    "url": "https://arxiv.org/abs/2601.08789",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "eed5e62c-daed-4933-8e70-7bbcca2ed62d",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}