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We give a new construction of functors from the category of modules for theassociative algebras $A_n(V)$ and $A_g(V)$ associated with a vertex operatoralgebra $V$, defined by Dong, Li and Mason, to the category of admissible$V$-modules and admissible twisted $V$-modules, respectively, using the methoddeveloped in the joint work \cite{HY1} with Y.-Z. Huang. The functors werefirst constructed by Dong, Li and Mason, but the importance of the new method,as in \cite{HY1}, is that we can apply the method to study objects without thecommutator formula in the representation theory of vertex operator algebras.

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