{
  "annotation_id": "0e010a61-00bc-46be-9e76-eefb59c00554",
  "date_created": "2026-03-02T18:01:27.736000Z",
  "date_modified": "2026-03-02T18:01:27.736000Z",
  "file_hash": "768187581c51e93157a7a1bd6ab78e539703aa5d7f635fc454f57d5d87c9113a",
  "private": false,
  "record": {
    "abstract": "In this paper we try to define the higher dimensional analogues of vertex\nalgebras. In other words we define algebras which we hope have the same\nrelation to higher dimensional quantum field theories that vertex algebras have\nto one dimensional quantum field theories (or to ``chiral halves\u0027\u0027 of two\ndimensional quantum field theories). The main idea is to define \"vertex\ngroups\". Then classical vertex algebras turn out to be the same as \"associative\ncommutative algebras\" over the simplest nontrivial example of a vertex group.\nWe investigate commutative algebras over higher dimensional vertex groups, some\nof which seem to be closely related to (free) quantum field theories.",
    "arxiv_id": "q-alg/9706008",
    "authors": [
      "Richard E. Borcherds"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "journal_ref": "\"Topological field theory, primitive forms and related topics\",\n  Edited by M. Kashiwara, A. Matsuo, K. Saito, I. Satake. Birkhauser 1998. ISBN\n  0-8176-3975-6",
    "title": "Vertex algebras",
    "url": "https://arxiv.org/abs/q-alg/9706008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "dc3f55c0-316d-4e71-ab28-8ed3f541ac49",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}