| Project/Area Number |
10640008
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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 | Tokyo University of Agriculture & Technology |
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Principal Investigator |
TAMAGATA Kunio Tokyo University of Agriculture and Technology, Department of Technology, Professor, 工学部, 教授 (60015849)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOTE Ichiro Tokyo University of Agriculture and Technology, Department of Technology, Professor, 工学部, 教授 (60021888)
TASHIRO Yoshiaki Tokyo University of Agriculture and Technology, Department of Technology, Professor, 工学部, 教授 (00014928)
WADA Tomoyuki Tokyo University of Agriculture and Technology, Department of Technology, Professor, 工学部, 教授 (30134795)
KAWATA Shigeto Tokyo University of Agriculture and Technology, Department of Mathematics, Associate Professor, 工学部, 助教授 (50195103)
MAEDA Hironobu Tokyo University of Agriculture and Technology, Department of Technology, Associate Professor, 工学部, 助教授 (50173711)
浅芝 秀人 大阪市立大学, 理学部, 助教授 (70175165)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 1999: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1998: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | finite dimensional algebra / representation / quiver / Frobenius algebra / symmetric algebra / module / 対称・多元環 / ホッホシルト拡大 / 2-コサイクル |
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| Research Abstract |
We studied representations of finite dimensional algebars over a field. In particular, we concentrated on the research of selfinjective algebas (ie Frobenius algebras). We got two main results. One is about a construction of symmetric algebras, and the other is a characterization of symmetric algebras induced from repetitive algebras by positive automorphism :
(1) Let L be a finite extension field of K. By using a given 2-cocycle of the K-algebra L, we constructed a 2-cocycle of the K-algebra LQ for an arbitrary finite quiver Q without oriented cycles, and we showed a criterion condition on L for all those K-algebras LQ to have symmetric non-splittable extension algebras defined by the 2-cocycles.
(2) Let BィイD4^ィエD4 be the repetitive algebra of a finite dimensional algebra B over a field K by the standard duality module over B, and let ν be the Nakayama automorphism of BィイD4^ィエD4. We determined the positive automorphisms ψ of BィイD4^ィエD4 such that the orbit algebra BィイD4^ィエD4/(ψν) is isomorphic to a splittable extension algebra of B by a minimal injective cogenerator, and we characterized weakly symmetric algebras and symmetric algebras, of the form BィイD4^ィエD4 /(ψν) with a positive automorphism ψ of BィイD4^ィエD4. As an application, we characterized some class of weakly symmetric algebras with non-periodic generalized standard Auslander-Reiten components.
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