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Frontiers of Mathematics in China

, Volume 14, Issue 5, pp 923–940 | Cite as

Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity

  • Xiaoshan Qin
  • Yanhua Wang
  • James ZhangEmail author
Research Article
  • 4 Downloads

Abstract

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.

Keywords

Noncommutative quasi-resolution Artin-Schelter regular algebra Maximal Cohen-Macaulay module pretzeled quivers 

MSC

16E65 16S38 14A22 

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Notes

Acknowledgements

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. [2016]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. [2016]3009). J. J. Zhang was partially supported by the US National Science Foundation (Grant No. DMS-1700825).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.China Academy of Electronics and Information TechnologyBeijingChina
  2. 2.School of Mathematical Sciences, Shanghai Center for Mathematical SciencesFudan UniversityShanghaiChina
  3. 3.School of Mathematics, Shanghai Key Laboratory of Financial Information TechnologyShanghai University of Finance and EconomicsShanghaiChina
  4. 4.Department of MathematicsUniversity of WashingtonSeattleUSA

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