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

We give a new construction of functors from the category of modules for the associative algebras An(V)An(V) and Ag(V)Ag(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 [5] with Y.-Z. Huang. The functors were first constructed by Dong, Li and Mason, but the importance of the new method, as in [5], is that we can apply the method to study objects without the commutator formula in the representation theory of vertex operator algebras.