Cluster-Cyclic Quivers with Three Vertices and the Markov Equation
Cluster-Cyclic Quivers with Three Vertices and the Markov Equation
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三顶点簇循环箭袋和马尔可夫方程
DOI：
10.1007/s10468-009-9179-9
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发表时间：
2006
影响因子：
0.6
通讯作者：
L. Hille
中科院分区：
文献类型：
--
作者：
A. Beineke;T. Brüstle;L. Hille
非循环簇代数具有关于由遗传代数定义的Calabi-Yau范畴中的倾斜对象的解释。因此，对于给定的箭图Q，需要确定由Q定义的簇代数是否是非循环的。在这种情况下，我们称Q为无环簇状，否则称为簇状循环。本文利用马尔可夫研究的丢番图方程，对具有三个顶点的簇循环箭图进行了分类。
Acyclic cluster algebras have an interpretation in terms of tilting objects in a Calabi-Yau category defined by some hereditary algebra. For a given quiver Q it is thus desirable to decide if the cluster algebra defined by Q is acyclic. We call Q cluster-acyclic in this case, otherwise cluster-cyclic. In this note we classify the cluster-cyclic quivers with three vertices using a Diophantine equation studied by Markov.