dorsal/arxiv
View SchemaA theory of tensor products for module categories for a vertex operator algebra, III
| Authors | Yi-Zhi Huang, James Lepowsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505018 |
| URL | https://arxiv.org/abs/q-alg/9505018 |
| Journal | J.Pure Appl.Algebra 100 (1995) 141-172 |
Abstract
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a suitable vertex operator algebra. The notion of vertex tensor category is essentially a ``complex analogue'' of the notion of symmetric tensor category, and in fact a vertex tensor category produces a braided tensor category in a natural way. In this paper, we focus on a particular element $P(z)$ of a certain moduli space of three-punctured Riemann spheres; in general, every element of this moduli space will give rise to a notion of tensor product, and one must consider all these notions in order to construct a vertex tensor category. Here we present the fundamental properties of the $P(z)$-tensor product of two modules for a vertex operator algebra. We give two constructions of a $P(z)$-tensor product, using the results, established in Parts I and II of this series, for a certain other element of the moduli space. The definitions and results in Part I (hep-th/9309076, which has been replaced by a new version with a greatly expanded introduction and updated references) and Part II (hep-th/9309159) are recalled.
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"abstract": "This is the third part in a series of papers developing a tensor product\ntheory for modules for a vertex operator algebra. The goal of this theory is to\nconstruct a ``vertex tensor category\u0027\u0027 structure on the category of modules for\na suitable vertex operator algebra. The notion of vertex tensor category is\nessentially a ``complex analogue\u0027\u0027 of the notion of symmetric tensor category,\nand in fact a vertex tensor category produces a braided tensor category in a\nnatural way. In this paper, we focus on a particular element $P(z)$ of a\ncertain moduli space of three-punctured Riemann spheres; in general, every\nelement of this moduli space will give rise to a notion of tensor product, and\none must consider all these notions in order to construct a vertex tensor\ncategory. Here we present the fundamental properties of the $P(z)$-tensor\nproduct of two modules for a vertex operator algebra. We give two constructions\nof a $P(z)$-tensor product, using the results, established in Parts I and II of\nthis series, for a certain other element of the moduli space. The definitions\nand results in Part I (hep-th/9309076, which has been replaced by a new version\nwith a greatly expanded introduction and updated references) and Part II\n(hep-th/9309159) are recalled.",
"arxiv_id": "q-alg/9505018",
"authors": [
"Yi-Zhi Huang",
"James Lepowsky"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"journal_ref": "J.Pure Appl.Algebra 100 (1995) 141-172",
"title": "A theory of tensor products for module categories for a vertex operator algebra, III",
"url": "https://arxiv.org/abs/q-alg/9505018"
},
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