| 研究課題/領域番号 |
18K03238
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分11010:代数学関連
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| 研究機関 | 名古屋大学 |
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研究代表者 |
ダルポ エリック 名古屋大学, 国際本部, 准教授 (00785959)
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| 研究期間 (年度) |
2018-04-01 – 2023-03-31
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| 研究課題ステータス |
完了 (2022年度)
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| 配分額 *注記 |
4,420千円 (直接経費: 3,400千円、間接経費: 1,020千円)
2020年度: 1,170千円 (直接経費: 900千円、間接経費: 270千円)
2019年度: 1,560千円 (直接経費: 1,200千円、間接経費: 360千円)
2018年度: 1,690千円 (直接経費: 1,300千円、間接経費: 390千円)
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| キーワード | 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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| 研究実績の概要 |
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.
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