Abstract
In this paper, we associate quantum vertex algebras to a certain family of associative algebras A˜(g) which are essentially Ding–Iohara algebras. To do this, we introduce another closely related family of associative algebras A(h). The associated quantum vertex algebras are based on the vacuum modules for A(h), whereas ϕ-coordinated modules for these quantum vertex algebras are associated to A˜(g)-modules. Furthermore, we classify their irreducible ϕ-coordinated modules.
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