Toroidal extended affine Lie algebras and vertex algebras

Abstract

In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their $\varphi$-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and $\varphi$-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of irreducible modules for the variant Lie algebras.

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• $(G,{\chi }_{\varphi })$-equivariant $\varphi$-coordinated modules for vertex algebras