Investigation into algebraic structure of the category of representations of finite demensional algebras
| Project/Area Number |
15540012
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | National University Corporation Tokyo University of Agriculture and Technology |
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Principal Investigator |
YAMAGATA Kunio Tokyo University of Agriculture and Technology, Graduate School, Institute of Symbiotic Science and Technology, Professor, 大学院・共生科学技術研究部, 教授 (60015849)
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| Co-Investigator(Kenkyū-buntansha) |
WADA Tomoyuki Tokyo University of Agriculture and Technology, Graduate School, Institute of Symbiotic Science and Technology, Professor, 大学院・共生科学技術研究部, 教授 (30134795)
YOSHINO Yuji Okayama University, Department of Mathematics, Professor, 理学部, 教授 (00135302)
ASASHIBA Hideto Osaka City University, Graduate School Science, Associate Professor, 大学院・理学研究科, 助教授 (70175165)
IYAMA Osamu Nagoya University, Graduate School of Mathematics, Asociate Professor, 大学院・多元数理科学研究科, 助教授 (70347532)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2005: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2004: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2003: ¥1,600,000 (Direct Cost: ¥1,600,000)
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| Keywords | finite dimensional algebra / self-injective algebra / Frobenius algebra / category / representation / module / クイバー |
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| Research Abstract |
The aim of the project is to study algebraic structures of the category of representations of finite dimensional algebras.
(1) We studied the stable categories of the algebras with Galois coveings by repetitive algebras, and proved the invariance of the property that a self-injecitve algebra has a Galois covering by the repetitive algebra of a quasi-tilted algebra.
(2) We studied non-Frobenius self-injecitve (=quasi-Frobenius) algebras, so that we found a characterization of those algebras and showed an example of non-Frobenius self-injective algebras with arbitrarily large dimension. By this example, we know that the example given by Nakayama in 1939 is the one with the smallest dimension.
(3) It is an open problem when an algebra has a preinjective component. We studied the problem for one-point extension algebras. We clarified that the existence of preinjective components of a one-point extension depends on AR-components where summands of the module defining the extension belong.
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Report
(4 results)
Research Products
(16 results)
