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

2016/07/23 by Chan, Kenneth, Kirkman, Ellen, Walton, Chelsea +1 · 2 citations
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1607.06977

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 A^H under such an action arises an analogue of a coordinate ring of a Kleinian singularity.

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• Commonly Graded Algebras and Their Homological Properties
• Quantum-symmetric equivalence for superpotential algebras

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