THE CLUSTER CATEGORY OF A CANONICAL ALGEBRA
THE CLUSTER CATEGORY OF A CANONICAL ALGEBRA
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DOI：
10.1090/s0002-9947-10-04998-6
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发表时间：
2008-01
影响因子：
1.3
通讯作者：
M. Barot;D. Kussin;H. Lenzing
中科院分区：
文献类型：
--
作者：
M. Barot;D. Kussin;H. Lenzing
利用加权射影线X上凝聚层的遗传范畴研究了典型代数A的簇范畴。作为应用，我们确定了簇范畴的自同构群，并证明了簇倾斜对象形成Buan，Iyama，Reiten和Scott意义上的簇结构。层范畴的倾斜图总是与簇范畴的倾斜图或交换图重合。我们表明，如果X的欧拉特征是非负的，或者等价地，如果A是驯服（国内或管状）表示类型，这个图是连接的。
We study the cluster category of a canonical algebra A in terms of the hereditary category of coherent sheaves over the corresponding weighted projective line X. As an application we determine the automorphism group of the cluster category and show that the cluster-tilting objects form a cluster structure in the sense of Buan, Iyama, Reiten and Scott. The tilting graph of the sheaf category always coincides with the tilting or exchange graph of the cluster category. We show that this graph is connected if the Euler characteristic of X is non-negative, or equivalently, if A is of tame (domestic or tubular) representation type.