dorsal/arxiv
View SchemaA theory of tensor products for module categories for a vertex operator algebra, IV
| Authors | Yi-Zhi Huang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505019 |
| URL | https://arxiv.org/abs/q-alg/9505019 |
| Journal | J.Pure Appl.Algebra 100 (1995) 173-216 |
Abstract
This is the fourth part of a series of papers developing a tensor product theory of modules for a vertex operator algebra. In this paper, We establish the associativity of $P(z)$-tensor products for nonzero complex numbers $z$ constructed in Part III of the present series under suitable conditions. The associativity isomorphisms constructed in this paper are analogous to associativity isomorphisms for vector space tensor products in the sense that it relates the tensor products of three elements in three modules taken in different ways. The main new feature is that they are controlled by the decompositions of certain spheres with four punctures into spheres with three punctures using a sewing operation. We also show that under certain conditions, the existence of the associativity isomorphisms is equivalent to the associativity (or (nonmeromorphic) operator product expansion in the language of physicists) for the intertwining operators (or chiral vertex operators). Thus the associativity of tensor products provides a means to establish the (nonmeromorphic) operator product expansion.
{
"annotation_id": "dfd2a5ff-1685-4b95-9b52-82f2777d8ac2",
"date_created": "2026-03-02T18:01:24.719000Z",
"date_modified": "2026-03-02T18:01:24.719000Z",
"file_hash": "510d31483a532a7c1f03a089d24969e78b945a427810a3060e44d517415c9048",
"private": false,
"record": {
"abstract": "This is the fourth part of a series of papers developing a tensor product\ntheory of modules for a vertex operator algebra. In this paper, We establish\nthe associativity of $P(z)$-tensor products for nonzero complex numbers $z$\nconstructed in Part III of the present series under suitable conditions. The\nassociativity isomorphisms constructed in this paper are analogous to\nassociativity isomorphisms for vector space tensor products in the sense that\nit relates the tensor products of three elements in three modules taken in\ndifferent ways. The main new feature is that they are controlled by the\ndecompositions of certain spheres with four punctures into spheres with three\npunctures using a sewing operation. We also show that under certain conditions,\nthe existence of the associativity isomorphisms is equivalent to the\nassociativity (or (nonmeromorphic) operator product expansion in the language\nof physicists) for the intertwining operators (or chiral vertex operators).\nThus the associativity of tensor products provides a means to establish the\n(nonmeromorphic) operator product expansion.",
"arxiv_id": "q-alg/9505019",
"authors": [
"Yi-Zhi Huang"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"journal_ref": "J.Pure Appl.Algebra 100 (1995) 173-216",
"title": "A theory of tensor products for module categories for a vertex operator algebra, IV",
"url": "https://arxiv.org/abs/q-alg/9505019"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "53176541-ed8c-4066-b485-8f18a7105c0f",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}