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

K. Chan, E. Kirkman, C. Walton, J. J. Zhang

Research output: Contribution to journalArticlepeer-review

Abstract

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 AH under such an action arises as an analogue of a coordinate ring of a Kleinian singularity.

Original languageEnglish (US)
Pages (from-to)512-538
Number of pages27
JournalJournal of Algebra
Volume508
DOIs
StatePublished - Aug 15 2018

Keywords

  • Artin–Schelter regular algebras
  • Auslander's theorem
  • Hopf algebra action
  • McKay correspondence
  • McKay quiver
  • Trivial homological determinant

ASJC Scopus subject areas

  • Algebra and Number Theory

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