On triangulated orbit categories
On triangulated orbit categories
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DOI：
10.4171/dm/199
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发表时间：
2005-03
影响因子：
0.9
通讯作者：
B. Keller
中科院分区：
文献类型：
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作者：
B. Keller
我们证明了在一个良好的自等价下，遗传范畴的有界导出范畴的轨道范畴是正则三角化的。这回答了A的一个问题。布安河马什和我在他们与M. Reineke和G. Todorov关于倾斜理论和团代数之间联系的一个问题（与Caldero-Chapoton-Schiffler的工作密切相关）和H. Asashiba关于轨道类别。我们观察到，由此产生的三角轨道范畴提供了许多简单的例子与Calabi-Yau性质的三角范畴。其中包括投射模范畴在Happel-Preiser-Ringel意义上的广义Dynkin型预投射代数上，其三角结构可以追溯到Auslander-Reiten关于理性奇点的表示论方法的工作。
We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by A. Buan, R. Marsh and I. Reiten which appeared in their study with M. Reineke and G. Todorov of the link between tilting theory and cluster algebras (closely related to work by Caldero-Chapoton-Schiffler) and a question by H. Asashiba about orbit categories. We observe that the resulting triangulated orbit categories provide many easy examples of triangulated categories with the Calabi-Yau property. These include the category of projective modules over a preprojective algebra of generalized Dynkin type in the sense of Happel-Preiser-Ringel, whose triangulated structure goes back to Auslander-Reiten's work on the representation-theoretic approach to rational singularities.