Stable categories of higher preprojective algebras

作者：Iyama Osamu; Oppermann Steffen^*

来源：Advances in Mathematics, 2013, 244: 23-68.

DOI：10.1016/j.aim.2013.03.013

• Higher preprojective algebra
• Stable category
• n-cluster tilting
• n-representation finite algebra
• n-cluster category

We introduce (n + 1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is is-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 n is an element of {1, 2}) the results above still hold for the stable category of Cohen-Macaulay modules.

• 出版日期2013-9-10