Higher rank Bell--Rogalski algebras

TL;DR

This paper generalizes Bell and Rogalski's construction to create new $Z^n$-graded simple rings, extending TGWAs of type $(A_1)^n$, and classifies their weight modules, tensor products, and simplicity conditions.

Contribution

It introduces a new construction of $Z^n$-graded simple rings that broadens the scope of TGWAs and provides a detailed classification of their modules and properties.

Findings

New $Z^n$-graded simple rings constructed

Classification of weight modules in torsion-free orbits

Simplicity criteria established for these algebras

Abstract

We generalize a construction of Bell and Rogalski to realize new examples of $\mathbb{Z}^n$-graded simple rings. This construction also generalizes TGWAs of type $(A_1)^n$. In addition to considering basic properties of these algebras, we provide a classification of weight modules in the setting of torsion-free orbits, study their (twisted) tensor products, and provide a simplicity criterion.