Vertex operator algebras and associative algebras

Details Vertex operator algebras and associative algebras Vertex operator algebras and associative algebras

1996-12-05

arxiv.org/abs/q-alg/9612010v2

Mathematics

Quantum Algebra

26 pages, amslatex, a mistake is corrected

Scientific paper

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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