Extension of vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$

TL;DR

This paper classifies irreducible modules for the affine Nappi-Witten Lie algebra and explores extending its associated vertex operator algebra by an even lattice, revealing new structural insights.

Contribution

It provides a classification of irreducible restricted modules for $ abla_{H_4}$ and details the structure of the vertex algebra extension by a lattice, highlighting differences from Heisenberg algebra representations.

Findings

Classification of irreducible modules for $ abla_{H_4}$

Structure of the vertex algebra extension by lattice $L$

Distinct representation theory compared to Heisenberg algebras

Abstract

We classify the irreducible restricted modules for the affine Nappi-Witten Lie algebra $\hat{H}_{4}$ with some natural conditions. It turns out the representation theory of $\hat{H}_{4}$ is quite different from the theory of representations of Heisenberg algebras. We also study the extension of the vertex operator algebra $V_{\hat{H}_{4}}(\ell,0)$ by the even lattice $L$. We give the structure of the extension $V_{\hat{H}_{4}}(\ell,0)\otimes \C[L]$ and its irreducible modules via irreducible representations of $V_{\hat{H}_{4}}(\ell,0)$ viewed as a vertex algebra.