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Cluster theory through derived categories and self-injective algebras

通过派生范畴和自注入代数的聚类理论

基本信息

批准号：
18K03238
负责人：
ダルポエリック
金额：
$ 2.83万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2018
资助国家：
日本
起止时间：
2018-04-01 至 2023-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18K03238/
关键词：
silting cluster-tilting d-silting mutation Fractionally Calabi-Yau self-injective algebra periodic projective resolution fractionally Calabi-Yau trivial extension Derived category Cluster category Cluster tilting Silting cluste

项目摘要

An important problem in cluster-tilting theory and higher-dimensional Auslander-Reiten theory is to characterise all d-cluster-tilting subcategories in the derived category of an algebra. The research this year has studied this problem by studying the connection between cluster-tilting and silting in derived categories. Certain types of silting objects, called d-silting objects, are known to give rise to cluster-tilting subcategories. The research has focused on understanding under which circumstances a certain combinatorial operation, called mutation, preserves the property of being d-silting, and how the operation of cluster-tilting mutation relates to that of mutation of silting objects.

在集团倾斜理论和高维Auslander-Reiten理论中的一个重要问题是在代数的导范畴中包含所有d-集团倾斜子范畴。今年的研究通过研究派生类别中的集群倾斜和淤积之间的联系来研究这个问题。某些类型的淤积物，称为d-淤积物，已知会产生星团倾斜子类。研究重点是了解在什么情况下某种称为突变的组合操作保留了清淤的性质，以及集群倾斜突变的操作与淤积对象突变的操作如何相关。