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Noncommutative graded algebras of finite Cohen-Macaulay representation type


Author: Kenta Ueyama
Journal: Proc. Amer. Math. Soc. 143 (2015), 3703-3715
MSC (2010): Primary 16G50, 16S38, 16E65, 14A22
DOI: https://doi.org/10.1090/proc/12527
Published electronically: May 4, 2015
MathSciNet review: 3359563
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Abstract: Let $ A$ be an AS-Cohen-Macaulay algebra. We show that if $ A$ is of finite Cohen-Macaulay representation type, then $ A$ is a noncommutative graded isolated singularity. This is a noncommutative analogue of a well-known theorem of Auslander and is a generalization of Jørgensen's theorem. Besides, we give an example of a noncommutative quadric hypersurface of finite Cohen-Macaulay representation type in a quantum $ {\mathbb{P}}^3$ which is not a domain. We also give all indecomposable graded maximal Cohen-Macaulay modules over it explicitly.


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Additional Information

Kenta Ueyama
Affiliation: Department of Mathematics, Graduate School of Science, Shizuoka University, 836 Ohya, Suruga-ku, Shizuoka, 422-8529, Japan
Address at time of publication: Department of Mathematics, Faculty of Education, Hirosaki University, 1 Bunkyocho, Hirosaki, Aomori 036-8560, Japan
Email: skueyam@ipc.shizuoka.ac.jp, k-ueyama@hirosaki-u.ac.jp

DOI: https://doi.org/10.1090/proc/12527
Keywords: Finite Cohen-Macaulay representation type, graded isolated singularity, AS-Cohen-Macaulay algebras, noncommutative quadric hypersurfaces
Received by editor(s): October 27, 2013
Received by editor(s) in revised form: March 4, 2014, and April 1, 2014
Published electronically: May 4, 2015
Additional Notes: The author was supported by JSPS Fellowships for Young Scientists No. 23-2233
Communicated by: Harm Derksen
Article copyright: © Copyright 2015 American Mathematical Society

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