Pointed Hopf actions on quantum generalized Weyl algebras
arXiv:2102.00320 · doi:10.1016/j.jalgebra.2022.03.005
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.
arXiv commentMain theorems restated to better illustrate primary findings. To appear in Journal of Algebra
References in corpus (7)
- Automorphisms and isomorphism of quantum generalized Weyl algebras
- Actions of some pointed Hopf algebras on path algebras of quivers
- Discriminants of Taft algebra smash products and applications
- 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