Weight modules over Bell--Rogalski algebras

TL;DR

This paper investigates a class of $ abla$-graded algebras introduced by Bell and Rogalski, generalizing rank one GWAs, focusing on their ring-theoretic properties and classifying simple weight modules.

Contribution

It establishes ring-theoretic properties of Bell--Rogalski algebras and classifies their simple weight modules, extending understanding of their structure and connection to GWAs.

Findings

Classified simple weight modules in infinite orbit case

Provided partial classification for finite orbit case

Established key ring-theoretic properties of these algebras

Abstract

We study a class of $\mathbb{Z}$-graded algebras introduced by Bell and Rogalski. Their construction generalizes in large part that of rank one generalized Weyl algebras (GWAs). We establish certain ring-theoretic properties of these algebras and study their connection to GWAs. We classify the simple weight modules in the infinite orbit case and provide a partial classification in the case of orbits of finite order.