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

2022/03/22 by Chen, Fulin, Li, Huansheng, Yu, Nina
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2203.11641

Abstract

In this paper, for every ε∈ ℤ, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the ϕ_ε-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.

Related

• Toroidal extended affine Lie algebras and vertex algebras
• Vertex operator algebras and the representation theory of toroidal algebras
• Toroidal vertex algebras and their modules
• Irreducible Modules for Extended Affine Lie Algebras
• A category of modules for the full toroidal Lie algebra