{
  "annotation_id": "8814407c-bc29-4ec2-84a5-bbab2d2a042a",
  "date_created": "2026-03-02T18:01:28.418000Z",
  "date_modified": "2026-03-02T18:01:28.418000Z",
  "file_hash": "1ee462d5496cdd69aee59edc0f425468ba7df48ff51d5163127eda00d3e05f1a",
  "private": false,
  "record": {
    "abstract": "A notion of Cartan pairs as an analogy of vector fields in the realm of\nnoncommutative geometry has been proposed in q-alg/9609011 In this paper we\ngive an outline of the construction of a noncommutative analogy of the algebra\nof partial differential operators as well as its natural (Fock type)\nrepresentation. We shall also define co-universal vector fields and covariant\nderivatives.",
    "arxiv_id": "q-alg/9710006",
    "authors": [
      "Andrzej Borowiec"
    ],
    "categories": [
      "q-alg",
      "math-ph",
      "math.MP",
      "math.QA"
    ],
    "doi": "10.1023/A:1021697831180",
    "journal_ref": "Cech. J. Phys., 47 (1997) 1093",
    "title": "Vector Fields and Differential Operators: Noncommutative Case",
    "url": "https://arxiv.org/abs/q-alg/9710006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f90399c9-da97-4cae-bc26-262cf2764dc0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}