Bimodules and g-rationality of vertex operator algebras

This paper studies the twisted representations of vertex operator algebras. Let V be a vertex operator algebra and g an automorphism of V of finite order T. For any m, n epsilon 1/TZ+, an A(g,n)(V)-A(g,m)(V)-bimodule A(g,n,m)(V) is constructed. The collection of these bimodules determines any admissible g-twisted V-module completely. A Verma type admissible g-twisted V-module is constructed naturally from any A(g,m)(V)-module. Furthermore, it is shown with the help of bimodule theory that a simple vertex operator algebra V is g-rational if and only if its twisted associative algebra Ag(V) is semisimple and each irreducible admissible g-twisted V-module is ordinary.