{
  "annotation_id": "2d7943fe-7fd6-4070-9a0e-0240513b614d",
  "date_created": "2026-03-02T18:01:24.967000Z",
  "date_modified": "2026-03-02T18:01:24.967000Z",
  "file_hash": "3a1d04b5840aa0e66de7143e3566458b853fa1e5b010e8c3ea4e6d5786a50283",
  "private": false,
  "record": {
    "abstract": "A regular vertex operator algebra is a vertex operator algebra such that any\nweak module (without grading) is a direct sum of ordinary irreducible modules.\nIn this paper we give several sufficient conditions under which a rational\nvertex operator algebra is regular. We prove that the moonshine module vertex\noperator algebra $V^{\\natural},$ the vertex operator algebras $L(l,0)$\nassociated with the integrable representations of affine algebras of level $l,$\nthe vertex operator algebras $L(c_{p,q},0)$ associated with irreducible highest\nweight representations for the discrete series of the Virasoro algebra and the\nvertex operator algebras $V_L$ associated with positive definite even lattices\n$L$ are regular. Our result for $L(l,0)$ implies that any restricted integrable\nmodule of level $l$ for the corresponding affine Lie algebra is a direct sum of\nirreducible highest weight integrable modules. The space $V_L$ in general is a\nvertex algebra if $L$ is not positive definite. In this case we establish the\ncomplete reducibility of any weak module.",
    "arxiv_id": "q-alg/9508018",
    "authors": [
      "Chongying Dong",
      "Haisheng Li",
      "Geoffrey Mason"
    ],
    "categories": [
      "q-alg",
      "math.QA"
    ],
    "title": "Regularity of rational vertex operator algebras",
    "url": "https://arxiv.org/abs/q-alg/9508018"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5ba887b7-e7b0-47f0-aa5c-6d23c0cf2c1f",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}