Mckay correspondence for semisimple Hopf actions on regular graded algebras. I. (English) Zbl 1420.16018
Summary: In establishing a more general version of the McKay correspondence, we prove Auslander’s theorem for actions of semisimple Hopf algebras \(H\) on noncommutative Artin-Schelter regular algebras \(A\) of global dimension two, where \(A\) is a graded \(H\)-module algebra, and the Hopf action on \(A\) is inner faithful with trivial homological determinant. We also show that each fixed ring \(A^H\) under such an action arises as an analogue of a coordinate ring of a Kleinian singularity.
MSC:
| 16T05 | Hopf algebras and their applications |
| 16E10 | Homological dimension in associative algebras |
| 14B05 | Singularities in algebraic geometry |
Keywords:
Artin-Schelter regular algebras; Auslander’s theorem; Hopf algebra action; McKay correspondence; McKay quiver; trivial homological determinantReferences:
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