Non-Weight modules over affine Nappi-Witten Lie algebras

TL;DR

This paper classifies certain rank-one modules over the affine Nappi-Witten Lie algebra, providing a complete understanding of their structure and irreducibility conditions, and extends results to affine-Virasoro Nappi-Witten algebras.

Contribution

It offers the first complete classification of Cartan-free rank-one modules over affine Nappi-Witten Lie algebras and establishes irreducibility criteria, extending to affine-Virasoro cases.

Findings

Complete classification of Cartan-free rank-one modules over affine Nappi-Witten Lie algebra.

Necessary and sufficient conditions for module irreducibility.

Extension of classification results to affine-Virasoro Nappi-Witten Lie algebras.

Abstract

In this paper, we study the representation theory of affine Nappi-Witten Lie algebra $\widehat{H_4}$ corresponding to the Nappi-Witten Lie algebra $H_4$. We completely classify all Cartan-free modules of rank one for the Nappi-Witten Lie algebra $H_4$. With the help of Cartan free $H_4$ modules we classify all Cartan-free modules of rank one over affine Nappi Witten Lie algebra. We also give a necessary and sufficient condition for these modules to be irreducible. Finally as an application we classify Cartan free modules of rank one for affine-Virasoro Nappi-Witten Lie algebras.