Higher rank Bell--Rogalski algebras

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.