{
  "annotation_id": "b020bc14-212d-4e44-a353-8ddeddab0416",
  "date_created": "2026-03-02T18:01:24.956000Z",
  "date_modified": "2026-03-02T18:01:24.956000Z",
  "file_hash": "07b12d754cba09d065501e9a5702adf8a5944511e5a6336e429b695a1190f4a5",
  "private": false,
  "record": {
    "abstract": "Based on the vanishing of the second Hochschild cohomology group of the\nenveloping algebra of the Heisenberg algebra it is shown that differential\nalgebras coming from quantum groups do not provide a non-trivial deformation of\nquantum mechanics. For the case of a q-oscillator there exists a deforming map\nto the classical algebra. It is shown that the differential calculus on quantum\nplanes with involution, i.e. if one works in position-momentum realization, can\nbe mapped on a q-difference calculus on a commutative real space. Although this\ncalculus leads to an interesting discretization it is proved that it can be\nrealized by generators of the undeformed algebra and does not posess a proper\ngroup of global transformations.",
    "arxiv_id": "q-alg/9508014",
    "authors": [
      "Mathias Pillin"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1007/BF02101181",
    "journal_ref": "Commun. Math. Phys. 180 (1996) 23",
    "title": "On the deformability of Heisenberg algebras",
    "url": "https://arxiv.org/abs/q-alg/9508014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "26851134-bd2b-47e1-a51e-d43ca2782792",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}