Positive cluster complexes and <i>τ</i>-tilting simplicial complexes of cluster-tilted algebras of finite type
Positive cluster complexes and <i>τ</i>-tilting simplicial complexes of cluster-tilted algebras of finite type
复制标题
有限型簇倾斜代数的正簇复形和<i>τ</i>-倾斜单纯复形
DOI：
10.1080/00927872.2023.2173763
复制
发表时间：
2023
影响因子：
0.7
通讯作者：
Gyoda Yasuaki
中科院分区：
文献类型：
--
作者：
Gyoda Yasuaki
在本研究中，我们考虑正簇复合体，即簇复合体的完整子复合体，其顶点均为非初始簇变量。特别地，我们提供了一个由有限型突变引起的正簇络合物的面向量差异的公式。此外，我们明确地描述了特定的有限型正簇配合物，并计算了它们的面向量。我们还提供了一种利用这些结果计算有限型任意正簇复的面向量的方法。进一步，我们利用簇与支撑倾斜模之间的对应关系，将我们的结果应用于有限表示型簇倾斜代数的倾斜理论。
In this study, we consider the positive cluster complex, a full subcomplex of a cluster complex the vertices of which are all non-initial cluster variables. In particular, we provide a formula for the difference in face vectors of positive cluster complexes caused by a mutation for finite type. Moreover, we explicitly describe specific positive cluster complexes of finite type and calculate their face vectors. We also provide a method to compute the face vector of an arbitrary positive cluster complex of finite type using these results. Furthermore, we apply our results to the-tilting theory of cluster-tilted algebras of finite representation type using the correspondence between clusters and support-tilting modules.