Representations of group rings and Auslander-Reiten quivers

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400051
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Nagoya City University (2016-2017); Osaka City University (2014-2015)
• Principal Investigator: KAWATA Shigeto 名古屋市立大学, 大学院システム自然科学研究科, 教授 (50195103)
• Co-Investigator(Renkei-kenkyūsha): KANEDA Masaharu 大阪市立大学, 大学院理学研究科, 教授 (60204575) ; FURUSAWA Masaaki 大阪市立大学, 大学院理学研究科, 教授 (50294525) ; BABA Yoshitomo 大阪教育大学, 教育学部, 教授 (10201724)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 有限群 / 表現 / Auslander-Reiten有向グラフ

Outline of Final Research Achievements

Let G be a finite group and R a complete discrete valuation ring with residue class field k of positive characteristic. Suppose that a block B of the group ring RG is of infinite representation type. Let L be an indecomposable B-lattice, and let C be the stable component of the Auslander-Reiten quiver of B containing L. Assume that the reduced kG-module M of L is indecomposable. Then, we have proved that the tree class of C is A-infinity if L is of height 0. Also, we have shown that if L and M have the same vertex Q, then the vertex of C is Q.

Free Research Field

有限群の表現論