New development of representation theory of orders

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340004
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Nagoya University
• Principal Investigator: IYAMA Osamu 名古屋大学, 多元数理科学研究科, 教授 (70347532)
• 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)
• 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)
• Project Period (FY): 2012-04-01 – 2016-03-31
• 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

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.

Free Research Field

整環の表現論