Representations of group rings and Auslander-Reiten quivers
| Project/Area Number |
26400051
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Nagoya City University (2016-2017)
Osaka City University (2014-2015) |
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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)
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| 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)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 有限群 / 表現 / Auslander-Reiten有向グラフ / 有限群の表現 / Auslander-Reiten quiver |
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| 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.
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Report
(5 results)
Research Products
(7 results)
