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Research on clarifying algebraic structure of rings using each representation theory of algebras, group rings and Lie rings.

Research Project

Project/Area Number 11640019
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionYamanashi University

Principal Investigator

SATO Masahisa  Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (30143952)

Co-Investigator(Kenkyū-buntansha) IWANAGA Yasuo  Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (80015825)
MIYAMOTO Izumi  Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (60126654)
KURIHARA Mitsunobu  Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (50027372)
Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥3,200,000 (Direct Cost: ¥3,200,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1999: ¥1,700,000 (Direct Cost: ¥1,700,000)
KeywordsRing / Representation / Algebra / Lie Algebra / Noeterian Ring / Group ring / Association Scheme / Noetherian ring / association scheme
Research Abstract

[1999]
In Duality theory Sato studied the principle of Duality which exists in Commutative noetherian ring and analyzed it in the view point of general non-commutative ring theory. By using non-commutative ring theory method, he succeeded to find the essential principle that Duality exists. which was difficult to find in the case of commutative ring since several facts were mixed to be held one fact. Also he showed theses facts hold also in the case of non-commutative rings under some conditions.
Miyamoto studied about Association scheme which is notified recently and he decided these which has elements up to 22.
Iwanaga generalized Wakamatsu theorem, which is famous theorem in the field of the representation theory of algebras, with respect to Tilting algebra.
Kurihara advised on researched through discussion about the above studies.
[2000]
Sato studied global dimension of typical case of quasi-hereditary rings which had been introduced from the representation theory of Lie algebras. For the ring you make the endomorphism ring of direct sum of all modules of the ring modulo the power of its Jacobson radical, then this ring becomes quasi-hereditary. He completely find the structure of minimal projective resolution of simple modules of this endomorphism ring and using this properties, he created the way of construction of resolution of these modules. Also he proved the global dimension does not exceed the number of simple modules.
Miyamoto found the construction of groups which includes normalizer of permutation groups by using association scheme noticed as generalization of group rings.
Iwanaga continued the study of the generalization of Wakamatsu theorem.
Kurahara gave advises in the stand point of view of analysis through discussions.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (19 results)

All Other

All Publications (19 results)

  • [Publications] Masahisa Sato: "Some kind of Duality"Proc.of the 4th Symp.on Ring theory and Representation theory. 355-364 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Global Dimension of an Endomorphism ring of Semi-local module"未定.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Miyamoto: "Computing normalizer of permutation groups effective using isomorhisms of association schems"Symp.on Symbolic and Algebraic Computation. 220-224 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yasuo Iwanaga: "Notes on Wakamatsu's generalized tilting modules"信州大学教育学部紀要. 99. 155-166 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Miyamoto Akira Hanaki: "Classification of primitive association scheme of order up to 22"Kyushu J.Math.. 54. 81-86 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Some notes on reflexive modules"山梨大学教育学部研究報告. 49. 30-35 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Some kind of Duality"Proc.of the 4th Symp.on Ring theory and Representation theory Birkhauser, Boston. 355-364 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Global Dimension of an Endomorphism ring of Semi-local module"(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Some notes on reflexive modules, Mem.Liberal Arts and Educ."Yamanashi University. 47. *-17 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Miyamoto, Akira Hanaki: "Classification of primitive association scheme of order up to 22"Kyushu J.Math.. 54. 81-86

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yasuo Iwanaga: "Notes on Wakamatsu's generalized tilting modules"Proc.of the fac. of Education Shinshu University. 99. 155-166 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Izumi Miyamoto: "Computing normalizer of permutation groups effective using isomorhisms of association schemes"Symp.on Symbolic and Algebraic Computation. 220-224 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Masahisa Sato: "Some kind of Duality"Proc.of the 4th Symp.on Ring theory and Representation theory. 355-364 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masahisa Sato: "Global Dimension of an Endomorphism ring of Semi-local module"(未定).

    • Related Report
      2000 Annual Research Report
  • [Publications] Izumi Miyamoto: "Computing normalizer of permutation groups effective using isomorhisms of association schemes"Symp.on Symbolic and Algebraic Computation. 220-224 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Yasuo Iwanaga: "Notes on Wakamatsu's generalized tilting modules"信州大学教育学部紀要. 99. 155-166 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Masahisa Sato: "Some kind of Duality"Proc. of the 4th Japan-China-Korea Ring Theory Symposium. (未定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Akira Hanaki, Izumi Miyamoto: "Classification of primitive association scheme of order up to 22"Kyushu J. Math.. (未定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yasuo Iwanaga: "Notes on Wakamatsu's generalized tilted modules"信州大学教育学部紀要第99号. 99(未定). (2000)

    • Related Report
      1999 Annual Research Report

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Published: 1999-04-01   Modified: 2016-04-21  

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