φ-Coordinated modules for quantum vertex algebras and associative algebras

We study N-graded phi-coordinated modules for a general quantum vertex algebra V of a certain type in terms of an associative algebra (A) over tilde (V) introduced by Y.Z. Huang. Among the main results, we associate a sequence of associative algebras (A) over tilde (n)(V)for n is an element of N with (A) over tilde (0)(V) = (A) over tilde (V) and we establish a bijection between the set of equivalence classes of irreducible N-graded phi-coordinated V-modules and the set of isomorphism classes of irreducible (A) over tilde (V)-modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector. (C) 2017 Elsevier Inc. All rights reserved.