Twists of twisted generalized Weyl algebras

TL;DR

This paper investigates the structural properties of twisted generalized Weyl algebras (TGWAs), demonstrating their stability under specific algebraic operations and extending known results to a broader context, with applications to noetherian properties.

Contribution

It introduces graded twists and tensor products for TGWAs, proving their closure and generalizing cocycle equivalence results to this class.

Findings

TGWAs are closed under graded twists and tensor products under mild conditions

Extended cocycle equivalence results to TGWAs

Certain type A_2 TGWAs are proven to be noetherian

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.