{
  "annotation_id": "7bcfab06-c68b-451a-8584-5a1bf11d5494",
  "date_created": "2026-03-02T18:01:28.009000Z",
  "date_modified": "2026-03-02T18:01:28.009000Z",
  "file_hash": "6c7881f5d201eed99cba7f2141ba048ad6fe667033c7c54733fbcea7d4fbcd3b",
  "private": false,
  "record": {
    "abstract": "For a simple vertex operator algebra whose Virasoro element is a sum of\ncommutative Virasoro elements of central charge 1/2, two codes are introduced\nand studied. It is proved that such vertex operator algebras are rational. For\nlattice vertex operator algebras and related ones, decompositions into direct\nsums of irreducible modules for the product of the Virasoro algebras of central\ncharge 1/2 are explicitly described. As an application, the decomposition of\nthe moonshine vertex operator algebra is obtained for a distinguished system of\n48 Virasoro algebras.",
    "arxiv_id": "q-alg/9707008",
    "authors": [
      "C. Dong",
      "R. L. Griess Jr.",
      "G. Hoehn"
    ],
    "categories": [
      "q-alg",
      "hep-th",
      "math.QA"
    ],
    "doi": "10.1007/s002200050335",
    "journal_ref": "Comm. Math. Phys. 193 (1998), 407-448",
    "title": "Framed vertex operator algebras, codes and the moonshine module",
    "url": "https://arxiv.org/abs/q-alg/9707008"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "27d8fb47-7a34-4c8d-81fa-1b444860bad4",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}