| Project/Area Number |
24340004
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya University |
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Principal Investigator |
IYAMA Osamu 名古屋大学, 多元数理科学研究科, 教授 (70347532)
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| Co-Investigator(Kenkyū-buntansha) |
TAKAHASHI Ryo 名古屋大学, 多元数理科学研究科, 准教授 (40447719)
Demonet Laurent 名古屋大学, 多元数理科学研究科, 特任准教授 (70646124)
MORI Izuru 静岡大学, 理学研究科, 教授 (50436903)
MINAMOTO Hiroyuki 大阪府立大学, 理学研究科, 准教授 (50527885)
HERSCHEND Martin (HERSCHEND Maratin) 名古屋大学, 多元数理科学研究科, 准教授 (90624627)
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| Co-Investigator(Renkei-kenkyūsha) |
ITO Yukari 名古屋大学, 多元数理科学研究科, 准教授 (70285089)
NAKANISHI Tomoki 名古屋大学, 多元数理科学研究科, 教授 (80227842)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2015: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2012: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
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| Keywords | 高次元Auslander-Reiten理論 / τ傾理論 / 導来圏 / Cohen-Macaulay加群 / n無限表現型 / Geigle-Lenzing完全交叉環 / 団理論 / 非可換特異点解消 / 整環 / 前射影多元環 / 三角圏 / τ-rigid加群 / 団代数 / 非可換クレパント特異点解消 / 傾対象 / 準傾退化 / Calabi-Yau退化 / 団圏 / τ rigid有限多元環 / 台τ傾加群 / 重み付き射影直線 / 傾理論 / 有限表現型 / 標準多元環 / n正則加群 / 変異 |
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| Outline of Final Research Achievements |
I studied representation theory of orders mainly from a point of view of Auslander-Reiten theory and tilting theory. In addition to the following three major results, I gave a number of new results.
(1) We introduced tau-tilting theory, which completes classical tilting theory from a point of view of mutation. (2) We introduced n-representation infinite algebras, which are basic in higher dimensional Auslander-Reiten theory. (3) As a higher dimensional generalization of weighted projective lines, we introduced Geigle-Lenzing complete intersections and developed a basic theory.
These results were published in 22 papers (all of them were refereed). I gave 64 lectures in international or domestic conferences and seminars.
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