{
  "annotation_id": "39a1ecc0-723e-48c2-be47-5ad9991121a4",
  "date_created": "2026-03-02T18:01:24.705000Z",
  "date_modified": "2026-03-02T18:01:24.705000Z",
  "file_hash": "7f6e142cbe3ac70414227d4ab550adcfdaa5b8f2346e1e98dbe735922e092a22",
  "private": false,
  "record": {
    "abstract": "We study the problem of classifying all Poisson-Lie structures on the group\n$G_{\\infty}$ of formal diffeomorphisms of the real line $\\zR^{1}$ which leave\nthe origin fixed, as well as the extended group of diffeomorphisms\n$G_{0\\infty}\\supset G_{\\infty}$ whose action on $\\zR^{1}$ does not necessarily\nfix the origin. A complete local classification of all Poisson-Lie structures\non the groups $G_{\\infty}$ and $G_{0\\infty}$ is given. This includes a\nclassification of all Lie-bialgebra structures on the Lie algebra $\\Cal\nG_{\\infty}$ of $G_{\\infty}$, which we prove to be all of coboundary type, and a\nclassification of all Lie-bialgebra strucutures on the Lie algebra $\\Cal\nG_{0\\infty}$ (the Witt algebra) of $G_{0\\infty}$ which also turned out to be\nall of coboundary type. A large class of Poisson structures on the space\n$V_{\\lambda}$ of $\\lambda$-densities on the real line is found such that\n$V_{\\lambda}$ becomes a homogeneous Poisson space under the action of the\nPoisson-Lie group $G_{\\infty}$. We construct a series of quantum semigroups\nwhose quasiclassical limits are finite-dimensional Poisson-Lie factor groups of\n$G_{\\infty}$ and $G_{0\\infty}$.",
    "arxiv_id": "q-alg/9506008",
    "authors": [
      "Ognyan Stoyanov"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Poisson-Lie Structures on Infinite-Dimensional Jet Groups and Quantum   Groups Related to Them",
    "url": "https://arxiv.org/abs/q-alg/9506008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "441c9666-faa9-4981-ada5-92d315fefe71",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}