Representations of Twisted Toroidal Lie Algebras from Twisted Modules over Vertex Algebras

TL;DR

This paper constructs representations of twisted toroidal Lie algebras using twisted modules over affine and lattice vertex algebras, advancing the understanding of their structure and representations.

Contribution

It introduces a novel method to build representations of twisted toroidal Lie algebras from twisted modules over vertex algebras.

Findings

Constructed explicit representations of twisted toroidal Lie algebras.

Connected twisted modules over vertex algebras to Lie algebra representations.

Provided new tools for studying twisted algebraic structures.

Abstract

Given a simple finite-dimensional Lie algebra and an automorphism of finite order, one defines the notion of a twisted toroidal Lie algebra. In this paper, we construct representations of twisted toroidal Lie algebras from twisted modules over affine and lattice vertex algebras.