Automorphisms and isomorphism of quantum generalized Weyl algebras

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]

10 pages

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• Isomorphisms of some quantum spaces
• The discriminant criterion and automorphism groups of quantized algebras
• Growth of generalized Weyl algebras over polynomial algebras and Laurent polynomial algebras
• Reflexive hull discriminants and applications
• Fixed rings of quantum generalized Weyl algebras
• Discriminants and Automorphism Groups of Veronese subrings of skew polynomial rings
• On the automorphisms of quantum Weyl algebras
• Classification of twisted generalized Weyl algebras over polynomial rings
• Derivations of Quantum and Involution Generalized Weyl Algebras
• Pointed Hopf actions on quantum generalized Weyl algebras
• The discriminant controls automorphism groups of noncommutative algebras
• Skew derivations on generalized Weyl algebras
• The Automorphism Groups for a family of Generalized Weyl Algebras
• Algebra endomorphisms and Derivations of Some Localized Down-Up Algebras