Vertex operator algebras and associative algebras
Abstract
Let V be a vertex operator algebra. We construct a sequence of associative algebras An(V) (n=0,1,2,...) such that An(V) is a quotient of An+1(V) and a pair of functors between the category of An(V)-modules which are not An-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 An(V) are finite-dimensional semisimple algebras.
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