{
  "annotation_id": "eb6b8620-6300-4cb0-b72e-09374d18501a",
  "date_created": "2026-03-02T18:01:25.081000Z",
  "date_modified": "2026-03-02T18:01:25.081000Z",
  "file_hash": "362b768c8ceca0ab89ca5ad35ee4f502259d87ad6d9c2e3a8ba11c07ddc1eb3b",
  "private": false,
  "record": {
    "abstract": "We proposed the construction of the differential calculus on the quantum\ngroup and its subgroup with the property of the natural reduction: the\ndifferential calculus on the quantum group $GL_q(2,C)$ has to contain the\ndifferential calculus on the quantum subgroup $SL_q(2,C)$ and quantum plane\n$C_q(2|0)$ (\u0027\u0027quantum matrjoshka\u0027\u0027). We found, that there are two differential\ncalculi, associated to the left differential Maurer--Cartan 1-forms and to the\nright differential 1-forms. Matched reduction take the degeneracy between the\nleft and right differentials. The classical limit ($q\\to 1$) of the \u0027\u0027left\u0027\u0027\ndifferential calculus and of the \u0027\u0027right\u0027\u0027 differential calculus is undeformed\ndifferential calculus. The condition ${\\cal D}_qG=1$ gives the differential\ncalculus on $SL_q(2,C)$, which contains the differential calculus on the\nquantum plane $C_q(2|0)$.",
    "arxiv_id": "q-alg/9509030",
    "authors": [
      "V. P. Akulov",
      "V. D. Gershun"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Matched differential calculus on the quantum groups   $GL_q(2,C),SL_q(2,C),C_q(2|0)$",
    "url": "https://arxiv.org/abs/q-alg/9509030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "583b5a95-0431-4757-a473-5a4a42347522",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}