Vertex operator algebras and associative algebras

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.

26 pages, amslatex, a mistake is corrected

References in corpus (1)

• Representation theory and tensor product theory for vertex operator algebras

Cited by in corpus (2)

• Twisted representations of vertex operator algebras and associative algebras
• On functors between module categories for associative algebras and for $\mathbb{N}$-graded vertex algebras