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arXiv · 2203.11641

Irreducible modules of toroidal Lie algebras arising from $\phi_\epsilon$-coordinated modules of vertex algebras

Fulin Chen·Huansheng Li·Nina Yu
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Abstract

In this paper, for every $\epsilon\in \mathbb{Z}$, we introduce an extension of the 2-toroidal Lie algebra by certain derivations. Based on the $\phi_\epsilon$-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 $\epsilon=1$, this affords a realization of certain irreducible modules for the toroidal extended affine Lie algebras first constructed by Billig.

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Fulin Chen, Huansheng Li, Nina Yu. 2022-03-22. Irreducible modules of toroidal Lie algebras arising from $\phi_\epsilon$-coordinated modules of vertex algebras. https://arxiv.org/abs/2203.11641

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