Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity
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We study properties of graded maximal Cohen-Macaulay modules over an ℕ-graded locally finite, Auslander Gorenstein, and Cohen-Macaulay algebra of dimension two. As a consequence, we extend a part of the McKay correspondence in dimension two to a more general setting.
KeywordsNoncommutative quasi-resolution Artin-Schelter regular algebra Maximal Cohen-Macaulay module pretzeled quivers
MSC16E65 16S38 14A22
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The authors thank the referees for the careful reading and very useful suggestions and thank Ken Brown, Daniel Rogalski, Robert Won, and Quanshui Wu for many useful conversations and valuable comments on the subject. Y. -H.Wang and X. -S. Qin thank the Department of Mathematics, University of Washington for its very supportive hospitality during their visits. X. -S. Qin was partially supported by the Foundation of China Scholarship Council (Grant No. 3100). Y. -H. Wang was partially supported by the National Natural Science Foundation of China (Grant Nos. 11971289, 11871071), the Foundation of Shanghai Science and Technology Committee (Grant No. 15511107300), and the Foundation of China Scholarship Council (Grant No. 3009). J. J. Zhang was partially supported by the US National Science Foundation (Grant No. DMS-1700825).
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