{
  "annotation_id": "ac9d90d7-c98d-4013-b68c-38d1c26cc543",
  "date_created": "2026-03-02T18:01:27.747000Z",
  "date_modified": "2026-03-02T18:01:27.747000Z",
  "file_hash": "57ce4cc887ce748c7df7393524f7403b86e0467667c745a343d3c68ba33d599f",
  "private": false,
  "record": {
    "abstract": "Recently V.Drinfeld formulated a number of problems in quantum group theory.\nIn particular, he suggested to consider ``set-theoretical\u0027\u0027 solutions of the\nquantum Yang-Baxter equation, i.e. solutions given by a permutation $R$ of the\nset $X\\times X$, where $X$ is a fixed finite set. In this note we study such\nsolutions, which satisfy the unitarity and the crossing symmetry conditions --\nnatural conditions arising in physical applications. More specifically, we\nconsider ``linear\u0027\u0027 solutions: the set $X$ is an abelian group, and the map $R$\nis an automorphism of $X\\times X$. We show that in this case, solutions are in\n1-1 correspondence with pairs $a,b\\in \\End X$, such that $b$ is invertible and\n$bab^{-1}=\\frac{a}{a+1}$. Later we consider ``affine\u0027\u0027 solutions ($R$ is an\nautomorphism of $X\\times X$ as a principal homogeneous space), and show that\nthey have a similar classification. The fact that these classifications are so\nnice leads us to think that there should be some interesting structure hidden\nbehind this problem.",
    "arxiv_id": "q-alg/9707027",
    "authors": [
      "Pavel Etingof",
      "Travis Schedler",
      "Alexandre Soloviev"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "On set-theoretical solutions of the quantum Yang-Baxter equation",
    "url": "https://arxiv.org/abs/q-alg/9707027"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "da61fd1d-9172-487a-93de-37d82d7566e8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}