Automorphisms and isomorphism of quantum generalized Weyl algebras

TL;DR

This paper classifies quantum generalized Weyl algebras up to isomorphism and determines their automorphism groups uniformly, including cases where the parameter q is a root of unity, thus completing previous classification results.

Contribution

It provides a comprehensive classification and automorphism group determination for quantum generalized Weyl algebras, extending prior work to include root of unity cases.

Findings

Complete classification of quantum generalized Weyl algebras up to isomorphism.

Determination of automorphism groups for all cases, including roots of unity.

Unified approach that extends previous partial results.

Abstract

We classify up to isomorphism the quantum generalized Weyl algebras and determine their automorphism groups in all cases in a uniform way, including those where the parameter q is a root of unity, thereby completing the results obtained by [Bavula, V. V.; Jordan, D. A. Isomorphism problems and groups of automorphisms for generalized Weyl algebras. Trans. Amer. Math. Soc. 353 (2001), no. 2, 769-794] and [Richard, L.; Solotar, A. Isomorphisms between quantum generalized Weyl algebras. J. Algebra Appl. 5 (2006), no. 3, 271-285]