McKay correspondence for semisimple Hopf actions on regular graded algebras, I.

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. [ABSTRACT FROM AUTHOR]