有序交换图
Ordered Exchange Graphs
AI总结：
本文公理化了表示论中由挠对、t-结构、silting对象等构成的有序交换图结构，将其作为Happel和Unger倾斜模偏序集的推广与完备化，并展示了多种构造及其相互联系。
摘要：
簇代数的交换图编码了簇的突变的组合学。通过近期使用表示论对簇代数的“范畴化”，人们获得了与各种对象相关联的大量交换图，例如有限维代数或集中在非正度数上的微分分次代数。这些构造通常源自倾斜概念的变化，交换图的顶点为挠对、t-结构、silting对象、支撑$τ$-倾斜模等。所有这些源于表示论的交换图都有一个额外特征，即它们是为这些对象自然定义的偏序的Hasse箭图。在这个意义上，本文研究的交换图可以被视为Happel和Unger所研究的倾斜模偏序集的推广或完备化。本文的目标是对由此获得的有序交换图结构进行公理化，展示有序交换图的各种构造，并将它们相互联系起来。
英文摘要：
The exchange graph of a cluster algebra encodes the combinatorics of mutations of clusters. Through the recent "categorifications" of cluster algebras using representation theory one obtains a whole variety of exchange graphs associated with objects such as a finite-dimensional algebra or a differential graded algebra concentrated in non-positive degrees. These constructions often come from variations of the concept of tilting, the vertices of the exchange graph being torsion pairs, t-structures, silting objects, support $τ$-tilting modules and so on. All these exchange graphs stemming from representation theory have the additional feature that they are the Hasse quiver of a partial order which is naturally defined for the objects. In this sense, the exchange graphs studied in this article can be considered as a generalization or as a completion of the poset of tilting modules which has been studied by Happel and Unger. The goal of this article is to axiomatize the thus obtained structure of an ordered exchange graph, to present the various constructions of ordered exchange graphs and to relate them among each other.
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。
