dorsal/arxiv
View SchemaVirasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory
| Authors | Yi-Zhi Huang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505020 |
| URL | https://arxiv.org/abs/q-alg/9505020 |
Abstract
In the references [HL1]--[HL5] and [H1], a theory of tensor products of modules for a vertex operator algebra is being developed. To use this theory, one first has to verify that the vertex operator algebra satisfies certain conditions. We show in the present paper that for any vertex operator algebra containing a vertex operator subalgebra isomorphic to a tensor product algebra of minimal Virasoro vertex operator algebras (vertex operator algebras associated to minimal models), the tensor product theory can be applied. In particular, intertwining operators for such a vertex operator algebra satisfy the (nonmeromorphic) commutativity (locality) and the (nonmeromorphic) associativity (operator product expansion). Combined with a result announced in [HL4], the results of the present paper also show that the category of modules for such a vertex operator algebra has a natural structure of a braided tensor category. In particular, for any pair $p, q$ of relatively prime positive integers larger than $1$, the category of minimal modules of central charge $1-6\frac{(p-q)^{2}}{pq}$ for the Virasoro algebra has a natural structure of a braided tensor category.
{
"annotation_id": "b7f62fd6-8766-4669-9685-8b78b61e0975",
"date_created": "2026-03-02T18:01:24.455000Z",
"date_modified": "2026-03-02T18:01:24.455000Z",
"file_hash": "b336e959bc55c404043f705a984e4cedee05485e20713c414effd1887c2efb73",
"private": false,
"record": {
"abstract": "In the references [HL1]--[HL5] and [H1], a theory of tensor products of\nmodules for a vertex operator algebra is being developed. To use this theory,\none first has to verify that the vertex operator algebra satisfies certain\nconditions. We show in the present paper that for any vertex operator algebra\ncontaining a vertex operator subalgebra isomorphic to a tensor product algebra\nof minimal Virasoro vertex operator algebras (vertex operator algebras\nassociated to minimal models), the tensor product theory can be applied. In\nparticular, intertwining operators for such a vertex operator algebra satisfy\nthe (nonmeromorphic) commutativity (locality) and the (nonmeromorphic)\nassociativity (operator product expansion). Combined with a result announced in\n[HL4], the results of the present paper also show that the category of modules\nfor such a vertex operator algebra has a natural structure of a braided tensor\ncategory. In particular, for any pair $p, q$ of relatively prime positive\nintegers larger than $1$, the category of minimal modules of central charge\n$1-6\\frac{(p-q)^{2}}{pq}$ for the Virasoro algebra has a natural structure of a\nbraided tensor category.",
"arxiv_id": "q-alg/9505020",
"authors": [
"Yi-Zhi Huang"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Virasoro vertex operator algebras, the (nonmeromorphic) operator product expansion and the tensor product theory",
"url": "https://arxiv.org/abs/q-alg/9505020"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "df23ddfb-951a-4f92-b286-d22841832ca2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}