MUTATION OF CLUSTER-TILTING OBJECTS AND POTENTIALS
MUTATION OF CLUSTER-TILTING OBJECTS AND POTENTIALS
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DOI：
10.1353/ajm.2011.0031
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发表时间：
2011-08-01
影响因子：
1.7
通讯作者：
Smith, D.
中科院分区：
文献类型：
--
作者：
Buan, A. B.;Iyama, O.;Smith, D.
我们证明了三角 2-Calabi-Yau 类别中簇倾斜物体的突变与势能箭袋的突变密切相关。这给出了 2-CY 倾斜代数和与势的颤动相关的雅可比代数之间的密切联系。我们证明簇倾斜代数是雅可比的，并且它们是由它们的颤动决定的。当处理 3-CY 代数上的倾斜模块时，也有类似的结果。 2-CY 倾斜代数的近 Morita 等价对于雅可比代数上的有限长度模成立。
We prove that mutation of cluster-tilting objects in triangulated 2-Calabi-Yau categories is closely connected with mutation of quivers with potentials. This gives a close connection between 2-CY-tilted algebras and Jacobian algebras associated with quivers with potentials.We show that cluster-tilted algebras are Jacobian and also that they are determined by their quivers. There are similar results when dealing with tilting modules over 3-CY algebras. The nearly Morita equivalence for 2-CY-tilted algebras is shown to hold for the finite length modules over Jacobian algebras.