2022 Fiscal Year Annual Research Report
Cluster theory through derived categories and self-injective algebras
| Project/Area Number |
18K03238
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| Research Institution | Nagoya University |
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Principal Investigator |
ダルポ エリック 名古屋大学, 国際本部, 准教授 (00785959)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | silting / cluster-tilting / d-silting / mutation |
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| Outline of Annual Research Achievements |
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.
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