Remarks on $ϕ$-coordinated modules for quantum vertex algebras

This paper is about $ϕ$-coordinated modules for weak quantum vertex algebras. Among the main results, several canonical connections among $ϕ$-coordinated modules for different $ϕ$ are established. For vertex operator algebras, a reinterpretation of Frenkel-Huang-Lepowsky's theorem on contragredient module is given in terms of $ϕ$-coordinated modules.

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