{
  "annotation_id": "14814e63-eb21-4580-a9a7-744b6b05dc5b",
  "date_created": "2026-03-02T18:02:48.238000Z",
  "date_modified": "2026-03-02T18:02:48.238000Z",
  "file_hash": "9b03321ac0a5ed4c38dc0a3553d4f921adf0484d011f4adb5a17c618a4d425db",
  "private": false,
  "record": {
    "abstract": "In this article we present all nonsingular upper triangular solutions to the\nconstant quantum Yang-Baxter equation\n$R_{j_1j_2}^{k_1k_2}R_{k_1j_3}^{l_1k_3}R_{k_2k_3}^{l_2l_3}=\nR_{j_2j_3}^{k_2k_3}R_{j_1k_3}^{k_1l_3}R_{k_1k_2}^{l_1l_2}$ in the three state\ncase, i.e. all indices ranging from 1 to 3. The upper triangular ansatz implies\n729 equations for 45 variables. Fortunately many of the equations turned out to\nbe simple allowing us to start breaking the problem into smaller ones. In the\nend we had a total of 552 solutions, but many of them were either inherited\nfrom two-state solutions or subcases of others. The final list contains 35\nnontrivial solutions, most of them new.",
    "arxiv_id": "solv-int/9306001",
    "authors": [
      "Jarmo Hietarinta"
    ],
    "categories": [
      "solv-int",
      "hep-th",
      "nlin.SI"
    ],
    "doi": "10.1088/0305-4470/26/23/044",
    "title": "The upper triangular solutions to the three-state constant quantum   Yang-Baxter equation",
    "url": "https://arxiv.org/abs/solv-int/9306001"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "fbcacdaa-53b1-4842-8b8c-d00a208cf2ad",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}