• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Study of algebras relating to quadratic form by using representation theory and homological algebras

Research Project

Project/Area Number 16540019
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionUniversity of Yamanashi

Principal Investigator

SATO Masahisa  University of Yamanashi, Department of Research Interdisciplinary Graduate School of Medicine and Engineering, Professor, 大学院医学工学総合研究部, 教授 (30143952)

Co-Investigator(Kenkyū-buntansha) IWANAGA Yasuo  Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (80015825)
WAKAMATSU Takayoshi  Saitama University, Faculty of Education, Professor, 教育学部, 教授 (00192435)
MIYAMOTO Izumi  University of Yamanashi, Department of Research Interdisciplinary Graduate School of Medicine and Engineering, Professor, 大学院医学工学総合研究部, 教授 (60126654)
Project Period (FY) 2004 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,600,000 (Direct Cost: ¥3,600,000)
Fiscal Year 2006: ¥600,000 (Direct Cost: ¥600,000)
Fiscal Year 2005: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2004: ¥1,800,000 (Direct Cost: ¥1,800,000)
Keywordsalgebra / quadratic form / representatuion theory / homology / cartan matrix / coxeter matrix / frobenius algebra / group / 環論 / ホモロジー代数 / 非可換代数幾何学 / 多元環の表現論 / 群論 / デライブ同値・ステーブル同値
Research Abstract

In 2004, we attended two international conference, the fourth Japan-China-Korea Iternational symposium on ting theory held in Nanjing, China from July 24 to 26 and the 11th International conference on representation theory of algebras to introduce the recent results and observe the trend of study.
In 2005, we held the 38th ring and representation theory symposium in Aichi Institute of Technology and we invited professor Raphael Rouquier (University Denis Diderot-Paris 7) who study closely related us and asked him lectures about elementary theory for solving Broue conjecture. These achievement are published as the proceedings.
In 2006, we invited professor Izuru Mori to ask lectures about non-commutative algebraic geometry, which is expected an important field of non-commutative ring theory, including its history and the trend in abroad. Also we invited Kiyoshi Igusa (Brandise, U. S. A) and Professor Yao Mushung (Fudan, China).
Through these research with many mathematicians, we completed the research of some kind of quadratic forms and we get the characterization to be the quadratic form corresponding to a Cartan matrix of an algebra. Also we characterized these conditions by the periodicity of a Coxeter matrix of a Cartan matrix of an algebra. As the result, we showed that the characteristic root of a Coxeter matrix is algebraic integer and this plays important role in these study.

Report

(4 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • Research Products

    (33 results)

All 2007 2006 2005 2004 Other

All Journal Article (29 results) Book (4 results)

  • [Journal Article] 「研究成果報告書概要(欧文)」より2007

    • Author(s)
      Masahisa Sato
    • Journal Title

      Yamagochih University Proceedings of Rings and related topics.(Yamanashih University)

      Pages: 82-82

    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An improvement of GAP Normalizer function for Permutation groups2006

    • Author(s)
      Miyamoto Izumi
    • Journal Title

      Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computations

      Pages: 234-238

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 算数科指導法の講義内容を検討する2006

    • Author(s)
      岩永恭雄
    • Journal Title

      信州大学教育学部附属実践センター紀要 7

      Pages: 101-110

    • NAID

      110006390533

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] improvement of GAP Normalizer function for permutation groups2006

    • Author(s)
      Izumi MiyamotoAn
    • Journal Title

      Proceedings of the 2006 International Symposium on ymbolic and Algebraic Computations

      Pages: 234-238

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] An improvement of GAP Normalizer function for permutation groups2006

    • Author(s)
      Miyamoto Izumi
    • Journal Title

      Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computations

      Pages: 234-238

    • Related Report
      2006 Annual Research Report
  • [Journal Article] 算数科指導法の講義内容を検討する2006

    • Author(s)
      岩本恭雄
    • Journal Title

      信州大学教育学部附属実線センター紀要 7

      Pages: 101-110

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Oneway hereditary rings2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      The Proc. Of the 10th InternationalSympo-sium on Ring and Representation Theory, Fields Institute 45

      Pages: 331-343

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Periodic Cartan Matrices and their associated Quadratic forms2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      Linear Algebras and its Applications 405

      Pages: 99-108

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2005 Annual Research Report
  • [Journal Article] On degenerations and splitting of exact sequences2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      Communication in algebra 33

      Pages: 2281-2298

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oneway hereditary rings2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      The Proc. of the 10th InternationalSympo-sium on Ring and Representation Theory. Fields Institute 45

      Pages: 331-343

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Periodic Cartan Matrices and their associated Quadratic form2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      Linear Algebras and its Applications

      Pages: 99-108

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 「研究成果報告書概要(欧文)」より2005

    • Author(s)
      Masahisa Sato, Takayoshi Wakamatsu
    • Journal Title

      Proceedings of 38th Ring and Representation theory symposium on ring theory

      Pages: 72-72

    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] 「研究成果報告書概要(欧文)」より2005

    • Author(s)
      Yasuo Iwanaga
    • Journal Title

      Linear Algebras(Nihon Hyouronsha)

      Pages: 264-264

    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Oneway hereditary rings2005

    • Author(s)
      Masahisa Sato
    • Journal Title

      The Proc.of the 10^<th> International Sympo-sium on Ring and Representation Theory, Fields Institute 45

      Pages: 331-343

    • Related Report
      2005 Annual Research Report
  • [Journal Article] 置換群の可移拡大の組合せ論的計算法2004

    • Author(s)
      宮本 泉
    • Journal Title

      第21回代数的組合せ論シンポジウム報告集 21

      Pages: 149-155

    • NAID

      40007193758

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] A combinatorial approach to doubiy transitive Permutation groups2004

    • Author(s)
      Izumi Miyamoto
    • Journal Title

      Proc. Of Conf. Association Schemes, and Designs

      Pages: 12-50

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] アソシエーションスキームの拡張と2重可移群の計算2004

    • Author(s)
      宮本 泉
    • Journal Title

      京都大学数理解析研究所報告集 1395

      Pages: 185-189

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Tilting modules and Auslander's Gorenstein Property2004

    • Author(s)
      Wakamatsu Takayoshi
    • Journal Title

      Journal of Algebra 275-1

      Pages: 3-39

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary 2004 Annual Research Report
  • [Journal Article] Stably equivalent but not derived equivalent symmetric algebra as induced from generalized tilting modules2004

    • Author(s)
      Wakamatsu Takayoshi
    • Journal Title

      第37回環論及び表現論シンポジウム報告集 37

      Pages: 113-115

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] combinatorial approach to doubly transitive Permutation groups2004

    • Author(s)
      Izumi MiyamotoA
    • Journal Title

      Proc. of Conf. Association Schemes, Codes, and Designs

      Pages: 12-50

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Tilting modules and Auslander's Gorenstein Property2004

    • Author(s)
      Takayoshi Wakamatsu
    • Journal Title

      Journal of Algebra 275-1

      Pages: 3-39

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Stably equivalent but not derived equivalent symmetric algebras induced from generalized tilting modules2004

    • Author(s)
      Takayoshi Wakamatsu
    • Journal Title

      Proceedings of 37th Ring and Representation theory symposium on ring theory

      Pages: 113-115

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] A combinatorial approach to doubly transitive Permutation groups2004

    • Author(s)
      Izumi Miyamoto
    • Journal Title

      Proc.of Conf.Association Schemes, Codes, and Designs

      Pages: 12-50

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stably equivalent but not derived equivalent symmetric algebras induced from generalized tilting modules2004

    • Author(s)
      Wakamatsu Takayoshi
    • Journal Title

      第37回環論および表現論シンポジウム報告集 37

      Pages: 113-115

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Stable Equivalences defined by generalized tilting modules2004

    • Author(s)
      Wakamatsu Takayoshi
    • Journal Title

      ICRA11報告集 11

      Pages: 41-42

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Periodic Cartan Matrices and their associated Quadratic forms

    • Author(s)
      Masahisa Sato
    • Journal Title

      Linear algebras and its applicaitons (未定)(掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On degenerations and splitting of exact sequences

    • Author(s)
      Masahisa Sato, Yousuke Ohnuki
    • Journal Title

      Communication in algebra (未定)(掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 置換群の可移拡大の組合せ論的計算法

    • Author(s)
      宮本 泉
    • Journal Title

      数式処理学会誌 (未定)(掲載決定)

    • NAID

      40007193758

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 置換群の可移拡大の計算法

    • Author(s)
      宮本 泉
    • Journal Title

      京都大学数理解析研究所報告集 (未定)(掲載決定)

    • Related Report
      2004 Annual Research Report
  • [Book] 「環とその周辺」報告集2007

    • Author(s)
      佐藤 眞久(編集)
    • Total Pages
      182
    • Publisher
      山口大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] 「環とその周辺」報告集2007

    • Author(s)
      佐藤眞久, 伊山修, 花木章秀(編集)
    • Total Pages
      182
    • Publisher
      山口大学
    • Related Report
      2006 Annual Research Report
  • [Book] 第38回環論および表現論シンポジューム報告集2006

    • Author(s)
      若松 隆義(編集)
    • Total Pages
      72
    • Publisher
      山梨大学
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Book] 入門線型代数学2005

    • Author(s)
      岩永 恭雄
    • Total Pages
      264
    • Publisher
      日本評論社
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary

URL: 

Published: 2004-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi