Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6425733 | Advances in Mathematics | 2013 | 46 Pages |
Abstract
We introduce (n+1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is n-representation-finite then its (n+1)-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)-preprojective algebra is (n+1)-Calabi-Yau, and, more precisely, it is the (n+1)-Amiot cluster category of the stable n-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)-cluster tilting object. We show that even if the (n+1)-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for nâ{1,2}) the results above still hold for the stable category of Cohen-Macaulay modules.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Osamu Iyama, Steffen Oppermann,