On associative algebras, modules and twisted modules for vertex operator algebras

Abstract

We give a new construction of functors from the category of modules for the associative algebras A n (V ) and A g (V ) associated with a vertex operator algebra V , defined by Dong, Li and Mason, to the category of admissible V -modules and admissible twisted V -modules, respectively, using the method developed in the joint work [HY1] with Y.-Z. Huang. The functors were first constructed by Dong, Li and Mason, but the importance of the new method, as in [HY1], is that we can apply the method to study objects without the commutator formula in the representation theory of vertex operator algebras.