{
  "annotation_id": "f83a33f9-158b-42cb-a78c-708f600feb78",
  "date_created": "2026-03-02T18:01:28.015000Z",
  "date_modified": "2026-03-02T18:01:28.015000Z",
  "file_hash": "571c4d344d3951326292f055af2d7991dd7fd45a0b28e35d1f06761b9f6c5bbf",
  "private": false,
  "record": {
    "abstract": "The classical Yang-Baxter equation (CYBE) is an algebraic equation central in\nthe theory of integrable systems. Its solutions were classified by Belavin and\nDrinfeld. Quantization of CYBE led to the theory of quantum groups. A geometric\ninterpretation of CDYB was given by Drinfeld and gave rise to the theory of\nPoisson-Lie groups. The classical dynamical Yang-Baxter equation (CDYBE) is an\nimportant differential equation analagous to CYBE and introduced by Felder as\nthe consistency condition for the Knizhnik-Zamolodchikov-Bernard equations for\ncorrelation functions in conformal field theory on tori. Quantization of CDYBE\nallowed Felder to introduce an interesting elliptic analog of quantum groups.\nIt becomes clear that numerous important notions and results connected with\nCYBE have dynamical analogs. In this paper we classify solutions to CDYBE and\ngive geometric interpretation to CDYBE. The classification and interpretation\nare remarkably analogous to the Belavin-Drinfeld picture.",
    "arxiv_id": "q-alg/9703040",
    "authors": [
      "Pavel Etingof",
      "Alexander Varchenko"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1007/s002200050292",
    "title": "Geometry and classification of solutions of the Classical Dynamical   Yang-Baxter Equation",
    "url": "https://arxiv.org/abs/q-alg/9703040"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dd48eab7-c10b-4bb1-8391-4ad4042618e1",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}