dorsal/arxiv
View SchemaVertex operator algebras and associative algebras
| Authors | Chongying Dong, Haisheng Li, Geoffrey Mason |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612010 |
| URL | https://arxiv.org/abs/q-alg/9612010 |
Abstract
Let V be a vertex operator algebra. We construct a sequence of associative algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V) and a pair of functors between the category of A_n(V)-modules which are not A_{n-1}(V)-modules and the category of admissible V-modules. These functors exhibit a bijection between the simple modules in each category. We also show that V is rational if and only if all A_n(V) are finite-dimensional semisimple algebras.
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"abstract": "Let V be a vertex operator algebra. We construct a sequence of associative\nalgebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V)\nand a pair of functors between the category of A_n(V)-modules which are not\nA_{n-1}(V)-modules and the category of admissible V-modules. These functors\nexhibit a bijection between the simple modules in each category. We also show\nthat V is rational if and only if all A_n(V) are finite-dimensional semisimple\nalgebras.",
"arxiv_id": "q-alg/9612010",
"authors": [
"Chongying Dong",
"Haisheng Li",
"Geoffrey Mason"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Vertex operator algebras and associative algebras",
"url": "https://arxiv.org/abs/q-alg/9612010"
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