@article{8cb8c7f7e2294f4c9f81632a9ead50ad,

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

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.",

keywords = "Artin–Schelter regular algebras, Auslander's theorem, Hopf algebra action, McKay correspondence, McKay quiver, Trivial homological determinant",

author = "K. Chan and E. Kirkman and C. Walton and Zhang, {J. J.}",

note = "Funding Information: The authors would like to thank W. Frank Moore for supplying corrections to some computations presented in Table 3, and we thank the referee for providing several helpful suggestions. C. Walton and J.J. Zhang were supported by the US National Science Foundation: NSF grants DMS-1550306, 1663775 and DMS-1402863 respectively. C. Walton is also supported by a research fellowship from the Sloan Foundation. E. Kirkman was supported by Simons Foundation Grant #208314. Funding Information: The authors would like to thank W. Frank Moore for supplying corrections to some computations presented in Table 3 , and we thank the referee for providing several helpful suggestions. C. Walton and J.J. Zhang were supported by the US National Science Foundation: NSF grants DMS-1550306 , 1663775 and DMS-1402863 respectively. C. Walton is also supported by a research fellowship from the Sloan Foundation . E. Kirkman was supported by Simons Foundation Grant # 208314 . Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

month = aug,

day = "15",

doi = "10.1016/j.jalgebra.2018.05.008",

language = "English (US)",

volume = "508",

pages = "512--538",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}