Pointed Hopf actions on quantum generalized Weyl algebras

Abstract

We study actions of pointed Hopf algebras in the $\ZZ$-graded setting. Our main result classifies inner-faithful actions of generalized Taft algebras on quantum generalized Weyl algebras which respect the $\ZZ$-grading. We also show that generically the invariant rings of Taft actions on quantum generalized Weyl algebras are commutative Kleinian singularities.

Main theorems restated to better illustrate primary findings. To appear in Journal of Algebra

References in corpus (4)

• Degree bounds for Hopf actions on Artin-Schelter regular algebras
• Actions of quantum linear spaces on quantum algebras
• Reflexive hull discriminants and applications
• Fixed rings of quantum generalized Weyl algebras