| Project/Area Number |
23540054
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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 | Osaka City University |
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Principal Investigator |
KAWATA Shigeto 大阪市立大学, 大学院理学研究科, 准教授 (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)
BABA Yoshitomo 大阪教育大学, 教育学部, 教授 (10201724)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Auslander-Reiten有向グラフ / 有限群の表現 / 概分裂列 |
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| Research Abstract |
Let RG be an integral group ring of a finite group G over a complete discrete valuation ring R with residue class field k of positive characteristic. Suppose that L is an indecomposable RG-lattice of height zero, and let S be a source of L. We have shown that the tree class of the Auslander-Reiten component containing L is A-infinity if and only if the tree class of the Auslander-Reiten component containing S is A-infinity. Also, we have proved that the middle term of the almost split sequence terminating in L is indecomposable if the reduced kG-module of L is indecomposable. In the case of 2-modular system, we have shown that the tree classes of the Auslander-Reiten components containing odd rank RG-lattices are A-infinity.
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