{
  "annotation_id": "fe1a3ead-f61c-4baa-8e64-b01f20264849",
  "date_created": "2026-03-02T18:01:28.128000Z",
  "date_modified": "2026-03-02T18:01:28.128000Z",
  "file_hash": "d6bf3326556b4c8b5e5683009def392aa26edd506f183ff7b5973ac14d4a7785",
  "private": false,
  "record": {
    "abstract": "In this paper we study associative algebras with a Poisson algebra structure\non the center acting by derivations on the rest of the algebra. These\nstructures, which we call Poisson fibred algebras, appear in the study of\nquantum groups at roots of 1 and related algebras, as well as in the\nrepresentation theory of affine Lie algebras at the critical level. Poisson\nfibred algebras lead to a generalization of Poisson geometry, which we develop\nin the paper. We also take up the general study of noncommutative spaces which\nare close to enough commutative ones so that they contain enough points to have\ninteresting commutative geometry. One of the most striking uses of our\nnoncommutative spaces is the quantum Borel-Weil-Bott Theorem for quantum sl_q\n(2) at a root of unity, which comes as a calculation of the cohomology of\nactual sheaves on actual topological spaces.",
    "arxiv_id": "q-alg/9606007",
    "authors": [
      "Nicolai Reshetikhin",
      "Alexander A. Voronov",
      "Alan Weinstein"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Semiquantum Geometry",
    "url": "https://arxiv.org/abs/q-alg/9606007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "167ee053-027d-490f-a25b-22b2bb2ae6de",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}