| 研究課題/領域番号 |
17F17814
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| 研究種目 |
特別研究員奨励費
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| 配分区分 | 補助金 |
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| 応募区分 | 外国 |
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| 研究分野 |
代数学
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| 研究機関 | 名古屋大学 |
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研究代表者 |
伊山 修 名古屋大学, 多元数理科学研究科, 教授 (70347532)
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| 研究分担者 |
WONG HON YIN 名古屋大学, 多元数理科学研究科, 外国人特別研究員
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| 研究期間 (年度) |
2017-11-10 – 2020-03-31
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| 研究課題ステータス |
完了 (2019年度)
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| 配分額 *注記 |
2,200千円 (直接経費: 2,200千円)
2019年度: 600千円 (直接経費: 600千円)
2018年度: 1,100千円 (直接経費: 1,100千円)
2017年度: 500千円 (直接経費: 500千円)
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| キーワード | Homological algebra / triangulated category / Perverse Equivalence / Torsion class / Mutation / Preprojective algebra / Symmetric Group Representations / Okuyama tilting complex / homological algebra / DG module / silting theory / Serre subcategory / torsion class / perverse equivalence / mutation / derived category / exact category / finite group algebras |
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| 研究実績の概要 |
With the help of the host we have investigate a type of perverse equivalence that correspond to two-term tilting. In general not all two-term tilting is a perverse equivalence. The condition of an algebra with all two-term tilting complex can be described using Jasso reduction. There is also an investigation into the particular case of preprojective algebra. In which we have determined the type of two-term tilting that is a perverse equivalence and related it to combinatorics of symmetric group.
Also we have established a link between Rouquier-Okuyama tilting complex to perverse equivalence, as suggested at the start of the project. There are still a lot of questions remain unanswered but we managed to get the results we hoped for.
Beside the above main progresses we have managed to conclude the work in homology of p-complexes of some symmetric group representations, a joint work with Aaron Chan in Nagoya University. The work with TUS is satisfactorily conducted.
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| 現在までの達成度 (段落) |
令和元年度が最終年度であるため、記入しない。
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| 今後の研究の推進方策 |
令和元年度が最終年度であるため、記入しない。
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