Non-weight modules over the BMS-Kac-Moody algebra

TL;DR

This paper constructs and classifies a new class of non-weight modules over the BMS-Kac-Moody algebra, detailing their irreducibility and isomorphism classes, expanding understanding of module structures in this algebra.

Contribution

It introduces a classification of non-weight modules over the BMS-Kac-Moody algebra that are free of rank one over the Cartan subalgebra's universal enveloping algebra.

Findings

Classification of non-weight modules over BMS-Kac-Moody algebra

Determination of irreducibility conditions

Identification of isomorphism classes

Abstract

In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give the classification of such modules. Moreover, the irreducibility and the isomorphism classes of these modules are determined.