Toroidal extended affine Lie algebras and vertex algebras (Q6634056)

The paper examines nullity-2 toroidal extended affine Lie algebras within the framework of vertex algebras and their \(\varphi\)-coordinated modules. It introduces a variant of toroidal extended affine Lie algebras and associates vertex algebras with these variant Lie algebras. Additionally, the paper establishes a canonical connection between modules for toroidal extended affine Lie algebras and \(\varphi\)-coordinated modules for the corresponding vertex algebras. By using some results from \textit{Y. Billig} [J. Algebra 308, No. 1, 252--269 (2007; Zbl 1113.17012); Can. J. Math. 59, No. 4, 712--729 (2007; Zbl 1166.17008)], the paper provides an explicit realization of a class of irreducible modules for the variant Lie algebras.