$\varphi$-coordinated modules for quantum vertex algebras and associative algebras

Abstract

We study $\mathbb{N}$-graded $\varphi$-coordinated modules for a general quantum vertex algebra $V$ of a certain type in terms of an associative algebra $\tilde{A}(V)$ introduced by Y.-Z. Huang. Among the main results, we establish a bijection between the set of equivalence classes of irreducible $\mathbb{N}$-graded $\varphi$-coordinated $V$-modules and the set of isomorphism classes of irreducible $\tilde{A}(V)$-modules. We also show that for a vertex operator algebra, rationality, regularity, and fusion rules are independent of the choice of the conformal vector.

36 pages

References in corpus (2)

• Constructing quantum vertex algebras
• Bimodules and g-rationality of vertex operator algebras