{
  "annotation_id": "47db53fc-b4e5-4b03-bdf4-41b39cab41fc",
  "date_created": "2026-03-02T18:01:27.734000Z",
  "date_modified": "2026-03-02T18:01:27.734000Z",
  "file_hash": "f7ee8462d0351b8c2d58d7d0ea9053016eab83d68ea6ce8617f58aecbce7e32a",
  "private": false,
  "record": {
    "abstract": "We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group\n$GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters\nand is split in two subalgebras: $U\u0027_{g,h}$ (with three generators) and $U(Z)$\n(with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of\n$U_{g,h}$. The subalgebra $U\u0027_{g,h}$ is not a Hopf subalgebra and its coalgebra\nstructure depends on both parameters. We discuss also two one-parameter special\ncases: $g =h$ and $g=-h$. The subalgebra $U\u0027_{h,h}$ is a Hopf algebra and\ncoincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The\nsubalgebra $U\u0027_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a\nnontrivial coalgebra structure and again is not a Hopf subalgebra of\n$U_{-h,h}$.",
    "arxiv_id": "q-alg/9705028",
    "authors": [
      "B. L. Aneva",
      "V. K. Dobrev",
      "S. G. Mihov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/30/19/016",
    "journal_ref": "J. Phys. A30 (1997) 6769-6781",
    "title": "Duality for the Jordanian Matrix Quantum Group $GL_{g,h}(2)$",
    "url": "https://arxiv.org/abs/q-alg/9705028"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c17c9755-1026-4c11-ad62-ed17fbd9548d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}