Intertwining operator algebras and vertex tensor categories for affine Lie algebras

Yi-Zhi Huang; James Lepowsky

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arXiv · q-alg/9706028

Intertwining operator algebras and vertex tensor categories for affine Lie algebras

Yi-Zhi Huang·James Lepowsky

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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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BibTeX RIS

Yi-Zhi Huang, James Lepowsky. 1999-03-24. Intertwining operator algebras and vertex tensor categories for affine Lie algebras. https://arxiv.org/abs/q-alg/9706028

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