Irreducible modules of toroidal Lie algebras arising from ϕϵ-coordinated modules of vertex algebras

Abstract

In this paper, for every ϵ∈Z, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the ϕϵ-coordinated modules theory for vertex algebras, we give an explicit realization of a class of irreducible highest weight modules for this extended toroidal Lie algebra. When ϵ=1, this affords a realization of certain irreducible modules for the toroidal extended affine Lie algebras first constructed by Billig.