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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 ε 1/T ℤ+, an Ag,n(V )-A g,m(V )-bimodule Ag,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 Ag,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. © 2008 American Mathematical Society.

Bimodules and $g$-rationality of vertex operator algebras