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

JOURNAL OF ALGEBRA

卷:508

Article

Chan, K.¹  Kirkman, E.²  Walton, C.³  Zhang, J. J.¹ 

[1] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

[2] Wake Forest Univ, Dept Math, POB 7388, Winston Salem, NC 27109 USA

[3] Univ Illinois, Dept Math, Urbana, IL 61801 USA

关键词: Artin-Schelter regular algebras;    Auslander's theorem;    Hopf algebra action;    McKay correspondence;    McKay quiver;    Trivial homological determinant;   

DOI  :  10.1016/j.jalgebra.2018.05.008

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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