{
  "annotation_id": "b1ed555a-be57-4c9f-8491-bed1d9d42f7f",
  "date_created": "2026-03-02T18:01:28.073000Z",
  "date_modified": "2026-03-02T18:01:28.073000Z",
  "file_hash": "559b26691e63e21b088e8cc52e28f436929415200cd4916b149e93b17a758ca8",
  "private": false,
  "record": {
    "abstract": "Let $\\hat{\\mathfrak{g}}$ be an untwisted affine Kac-Moody algebra, with its\nSklyanin-Drinfel\u0027d structure of Lie bialgebra, and let $\\hat{\\mathfrak{h}}$ be\nthe dual Lie bialgebra. By dualizing the quantum double construction - via\nformal Hopf algebras - we construct a new quantum group\n$U_q(\\hat{\\mathfrak{h}})$, dual of $U_q(\\hat{\\mathfrak{g}})$. Studying its\nrestricted and unrestricted integer forms and their specializations at roots of\n1 (in particular, their classical limits), we prove that\n$U_q(\\hat{\\mathfrak{h}})$ yields quantizations of $\\hat{\\mathfrak{h}}$ and\n$\\hat{G}^\\infty$ (the formal group attached to $\\hat{\\mathfrak{g}}$), and we\nconstruct new quantum Frobenius morphisms. The whole picture extends to the\nuntwisted affine case the results known for quantum groups of finite type.",
    "arxiv_id": "q-alg/9712013",
    "authors": [
      "Fabio Gavarini"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/s002090050502",
    "journal_ref": "Mathematische Zeitschrift 234 (2000), no. 1, 9-52",
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Dual Affine Quantum Groups",
    "url": "https://arxiv.org/abs/q-alg/9712013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f3198a89-e674-40fc-bdc1-ca5cf11a7804",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}