{
  "annotation_id": "83d1dd24-b7b2-4cbe-88c5-02724dfcf6d8",
  "date_created": "2026-03-02T18:01:28.821000Z",
  "date_modified": "2026-03-02T18:01:28.821000Z",
  "file_hash": "89c16930992543116b983e65b1265a98522b25f81d8ebbd9ec0b362613486c40",
  "private": false,
  "record": {
    "abstract": "The $h$-deformed quantum plane is a counterpart of the $q$-deformed one in\nthe set of quantum planes which are covariant under those quantum deformations\nof GL(2) which admit a central determinant. We have investigated the\nnoncommutative geometry of the $h$-deformed quantum plane. There is a\n2-parameter family of torsion-free linear connections, a 1-parameter sub-family\nof which are compatible with a skew-symmetric non-degenerate bilinear map. The\nskew-symmetric map resembles a symplectic 2-form and induces a metric. It is\nalso shown that the extended $h$-deformed quantum plane is a noncommutative\nversion of the Poincar\\\u0027e half-plane, a surface of constant negative Gaussian\ncurvature.",
    "arxiv_id": "q-alg/9709007",
    "authors": [
      "S. Cho",
      "J. Madore",
      "K. S. Park"
    ],
    "categories": [
      "q-alg",
      "gr-qc",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/31/11/013",
    "title": "Noncommutative Geometry of the h-deformed Quantum Plane",
    "url": "https://arxiv.org/abs/q-alg/9709007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "60cf5ae0-8ed2-43cd-8e15-019b295e6263",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}