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

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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.

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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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Authors and Affiliations

  1. China Academy of Electronics and Information Technology, Beijing, 100041, China

    Xiaoshan Qin

  2. School of Mathematical Sciences, Shanghai Center for Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Xiaoshan Qin

  3. School of Mathematics, Shanghai Key Laboratory of Financial Information Technology, Shanghai University of Finance and Economics, Shanghai, 200433, China

    Yanhua Wang

  4. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    James Zhang

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  1. Xiaoshan Qin
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  2. Yanhua Wang
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  3. James Zhang
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Correspondence to James Zhang.

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Qin, X., Wang, Y. & Zhang, J. Maximal Cohen-Macaulay modules over a noncommutative 2-dimensional singularity. Front. Math. China 14, 923–940 (2019). https://doi.org/10.1007/s11464-019-0793-5

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