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arxiv: 2102.00320 · v2 · pith:CD5K7SDCnew · submitted 2021-01-30 · 🧮 math.RA · math.QA

Pointed Hopf actions on quantum generalized Weyl algebras

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keywords algebrasactionsgeneralizedquantumweylhopfpointedtaft
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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.

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