dorsal/arxiv
View SchemaIntertwining operator algebras and vertex tensor categories for affine Lie algebras
| Authors | Yi-Zhi Huang, James Lepowsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706028 |
| URL | https://arxiv.org/abs/q-alg/9706028 |
Abstract
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the Wess-Zumino-Novikov-Witten models and related models in conformal field theory. We show that for the category of modules for a vertex operator algebra containing a subalgebra isomorphic to a tensor product of rational vertex operator algebras associated to affine Lie algebras, the intertwining operators among the modules have the associativity property, the category has a natural structure of vertex tensor category, and a number of related results hold. We obtain, as a corollary and special case, a construction of the previously-studied braided tensor category structure on the category of finite direct sums of standard (integrable highest weight) modules of a fixed positive integral level for an affine Lie algebra.
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"abstract": "We apply the general theory of tensor products of modules for a vertex\noperator algebra developed in our papers hep-th/9309076, hep-th/9309159,\nhep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of\nthe Wess-Zumino-Novikov-Witten models and related models in conformal field\ntheory. We show that for the category of modules for a vertex operator algebra\ncontaining a subalgebra isomorphic to a tensor product of rational vertex\noperator algebras associated to affine Lie algebras, the intertwining operators\namong the modules have the associativity property, the category has a natural\nstructure of vertex tensor category, and a number of related results hold. We\nobtain, as a corollary and special case, a construction of the\npreviously-studied braided tensor category structure on the category of finite\ndirect sums of standard (integrable highest weight) modules of a fixed positive\nintegral level for an affine Lie algebra.",
"arxiv_id": "q-alg/9706028",
"authors": [
"Yi-Zhi Huang",
"James Lepowsky"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"title": "Intertwining operator algebras and vertex tensor categories for affine Lie algebras",
"url": "https://arxiv.org/abs/q-alg/9706028"
},
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