{
  "annotation_id": "5797b090-4f7d-4f0e-9c00-708dfffbe3ca",
  "date_created": "2026-03-02T18:01:27.877000Z",
  "date_modified": "2026-03-02T18:01:27.877000Z",
  "file_hash": "d95d8da8a14aeb0580e420b7cc42033c30fbc1603722f06c54b133c069d482a9",
  "private": false,
  "record": {
    "abstract": "Lie bialgebra structures on $e(2)$ are classified. For two Lie bialgebra\nstructures which are not coboundaries (i.e. which are not determined by a\nclassical $r$-matrix) we solve the cocycle condition, find the Lie-Poisson\nbrackets and obtain quantum group relations. There is one to one correspondence\nbetween Lie bialgebra structures on $e(2)$ and possible quantum deformations of\n$U(e(2))$ and $E(2)$.",
    "arxiv_id": "q-alg/9603009",
    "authors": [
      "Jan Sobczyk"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1088/0305-4470/29/11/022",
    "title": "Quantum E(2) groups and Lie bialgebra structures",
    "url": "https://arxiv.org/abs/q-alg/9603009"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6cbd2f43-2178-46a6-9c36-ad71c021cf52",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}