Cluster theory through derived categories and self-injective algebras
| Project/Area Number |
18K03238
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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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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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 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 / cluster category / derived category / cluster tilting / 表現論 / クラスター代数 |
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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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Report
(5 results)
Research Products
(9 results)
