Vertex operator algebras and associative algebras

Chongying Dong; Haisheng Li; Geoffrey Mason

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arXiv · q-alg/9612010

Vertex operator algebras and associative algebras

Chongying Dong·Haisheng Li·Geoffrey Mason

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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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BibTeX RIS

Chongying Dong, Haisheng Li, Geoffrey Mason. 1997-01-15. Vertex operator algebras and associative algebras. https://arxiv.org/abs/q-alg/9612010

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