{
  "annotation_id": "10000cb3-74c1-42d8-bbdd-2ed3621645a5",
  "date_created": "2026-03-02T18:01:28.354000Z",
  "date_modified": "2026-03-02T18:01:28.354000Z",
  "file_hash": "08e98d7483fdcba46b38f40de9c8545959ae4152b343e3e5f8c6e7fb009a7745",
  "private": false,
  "record": {
    "abstract": "In this paper we define an algebra structure on the vector space $L(\\Sigma)$\ngenerated by links in the manifold $\\Sigma \\times [0,1]$ where $\\Sigma $ is an\noriented surface. This algebra has a filtration and the associated graded\nalgebra $L_{Gr}(\\Sigma)$ is naturally a Poisson algebra. There is a Poisson\nalgebra homomorphism from the algebra of chord diagrams $ch(\\Sigma)$ on $\\Sigma\n$ to $L_{Gr}(\\Sigma)$.\n  We show that multiplication in $L(\\Sigma)$ provides a geometric way to define\na deformation quantization of the algebra of chord diagrams, provided there is\na universal Vassiliev invariant for links in $\\Sigma\\times [0,1]$. The\nquantization descends to a quantization of the moduli space of flat connections\non $\\Sigma $ and it is universal with respect to group homomorphisms. If\n$\\Sigma $ is compact with free fundamental group we construct a universal\nVassiliev invariant.",
    "arxiv_id": "q-alg/9701018",
    "authors": [
      "J\u00f8rgen Ellegaard Andersen",
      "Josef Mattes",
      "Nicolai Reshetikhin"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "doi": "10.1017/S0305004198002813",
    "title": "Quantization of the Algebra of Chord Diagrams",
    "url": "https://arxiv.org/abs/q-alg/9701018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7e609470-310d-4392-b16c-616d28b84219",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}