{
  "annotation_id": "4f57f3ec-6c54-4b4a-9f07-5e61f08ac230",
  "date_created": "2026-02-17T05:53:15.903000Z",
  "date_modified": "2026-02-17T05:53:15.903000Z",
  "file_hash": "45046c64134ee71a394d4e3358d27da7be09d8c27e1f24234df4b5014c980ba1",
  "private": false,
  "record": {
    "abstract": "The Adler-Gelfand-Dikii Poisson structure arises naturally in the study of $n$-th order differential operators on the circle and plays a central role in Poisson geometry and integrable systems. Let $G$ be one of the Lie groups $\\mathrm{PSL}(n)$, $\\mathrm{PSp}(n)$ (for even $n$), or $\\mathrm{PSO}(n)$ (for odd $n$). In this paper, we construct the symplectic groupoid integrating the Adler-Gelfand-Dikii Poisson structure associated to $G$ and prove that it is Morita equivalent to the quasi-symplectic groupoid integrating the Dirac structure on $Y_n(\\mathbf{C})$, where $Y_n(\\mathbf{C})$ denotes the quotient of the space of quasi-periodic non-degenerate curves by homotopies preserving the monodromy.",
    "arxiv_id": "2601.08632",
    "authors": [
      "Ahmadreza Khazaeipoul"
    ],
    "categories": [
      "math.SG",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "The symplectic groupoid for Adler-Gelfand-Dikii Poisson structure",
    "url": "https://arxiv.org/abs/2601.08632",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "88c7f00c-aeb0-48c6-b552-c9121a79e0d8",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}