Rank-n Bell and Rogalski algebras are defined; they generalize twisted generalized Weyl algebras of type (A1)^n, and their simple weight modules on torsion-free orbits are classified.
Twists of twisted generalized Weyl algebras
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abstract
We study graded twisted tensor products and graded twists of twisted generalized Weyl algebras (TGWAs). We show that the class of TGWAs is closed under these operations assuming mild hypotheses. We generalize a result on cocycle equivalence amongst multiparameter quantized Weyl algebras to the setting of TGWAs. As another application we prove that certain TGWAs of type $A_2$ are noetherian.
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Higher rank Bell--Rogalski algebras
Rank-n Bell and Rogalski algebras are defined; they generalize twisted generalized Weyl algebras of type (A1)^n, and their simple weight modules on torsion-free orbits are classified.