Abstract
Let A be an AS-Cohen-Macaulay algebra. We show that if A is of finite CohenMacaulay 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 Jorgensen’s theorem. Besides, we give an example of a noncommutative quadric hypersurface of finite Cohen-Macaulay representation type in a quantum P which is not a domain. We also give all indecomposable graded maximal Cohen-Macaulay modules over it explicitly.
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