Ding–Iohara algebras and quantum vertex algebras.

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. [ABSTRACT FROM AUTHOR]