周期树与半不变量
Periodic trees and semi-invariants
摘要：
周期树是与仿射型簇范畴$\tilde{A}_{n-1}$中的簇倾斜对象双射的组合结构。树的内部边缘对与集群倾斜对象相对应的$c$向量以及与集群倾斜对象相关联的虚拟半不变量的权重进行编码。我们还显示了树的边缘的位置和集群倾斜对象的相应的和是否是预投射，预内射或定期之间的直接关系。
英文摘要：
Periodic trees are combinatorial structures which are in bijection with cluster tilting objects in cluster categories of affine type $\tilde{A}_{n-1}$. The internal edges of the tree encode the $c$-vectors corresponding to the cluster tilting object, as well as the weights of the virtual semi-invariants associated to the cluster tilting object. We also show a direct relationship between the position of the edges of the tree and whether the corresponding summands of the cluster tilting object are preprojective, preinjective or regular.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
