Twisted representations of vertex operator algebras and associative algebras

Abstract

Let V be a vertex operator algebra and g an automorphism of order T. We construct a sequence of associative algebras A_{g,n}(V) with n\in\frac{1}{T}\Z nonnegative such that A_{g,n}(V) is a quotient of A_{g,n+1/T}(V) and a pair of functors between the category of A_{g,n}(V)-modules which are not A_{g,n-1/T}(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 g-rational if and only if all A_{g,n}(V) are finite-dimensional semisimple algebras.