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A study of nonassociative algebras and mathematical physics

Research Project

Project/Area Number 19540042
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionThe University of Aizu

Principal Investigator

KAMIYA Norikaki (KAMIYA Noriaki)  The University of Aizu, コンピュータ理工学部, 教授 (90144691)

Co-Investigator(Kenkyū-buntansha) SUZUKI Taro  会津大学, コンピュータ理工学部, 准教授 (90272179)
MORI Kazuyoshi  会津大学, コンピュータ理工学部, 上級准教授 (20252322)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsリー環論 / 三項系代数 / リー代数 / 三項系 / 非結合的代数 / 環論 / 非結合的代数系
Research Abstract

A study of construction of G(3),F(4) D(m,n) from triple systems.
This construction is a mixed field of nonassociative algebras and math. Physics..
Historicaly speaking, we think that the origin is from Cartan Killing,Freudenthal, Jacobson etc. Our methods are a methods of means in without root system using.
That is, A classification of triple systems and Peirce decomposition, Nambu identity relations had considered.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (33 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (18 results) (of which Peer Reviewed: 18 results) Presentation (15 results)

  • [Journal Article] A structure theory of (-1,-1)Freudenthal-Kantor triple systems2010

    • Author(s)
      N.Kamiya
    • Journal Title

      Bull.Austrian Math vol.81

      Pages: 132-155

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] koukyuroku2010

    • Author(s)
      N.Kamiya
    • Journal Title

      RIMS 1712

      Pages: 10-20

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On Lie and Jordan structure associated with Freudenthal-Kantor triple systems2010

    • Author(s)
      神谷徳昭
    • Journal Title

      Mitt.Math.Ges.Hamburg

      Volume: 29 Pages: 109-123

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representationtation of triple ystems2010

    • Author(s)
      神谷徳昭
    • Journal Title

      Linear and Multilinear Algebras

      Volume: 58 Pages: 617-643

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A structure theory of Freudenthal-Kantor triple systems2010

    • Author(s)
      神谷徳昭
    • Journal Title

      Bull.Aust.Math.

      Volume: 81 Pages: 132-155

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On lie and gosdan structure of title systems2010

    • Author(s)
      N.Kamiya, S.Okuto
    • Journal Title

      Mitt.Math, Ges.Hamburg 29(印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rekneeentations of (α,β,γ)title systems2010

    • Author(s)
      N.Kamiya, S.Okuto
    • Journal Title

      Lineaz and Multilineaz Alg. (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Astructuso thery of (-1,-1)-title systems2010

    • Author(s)
      N.Kamiya, S.Okuto
    • Journal Title

      Bull.Aust.Math.Soc 81

      Pages: 132-155

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations of(α,β,γ)triple systems2010

    • Author(s)
      N.Kamiya, S Okubo
    • Journal Title

      Linear and Multilinear Alg. (印刷中)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] koukyuroku2009

    • Author(s)
      N.Kamiya
    • Journal Title

      RIMS 1655

      Pages: 56-65

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] koukyuroku2009

    • Author(s)
      N.Kamiya
    • Journal Title

      RIMS 1677

      Pages: 253-260

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new class of nonassociative algebras with involution, Proc.2008

    • Author(s)
      N.Kamiya
    • Journal Title

      Japan Acad

      Pages: 68-72

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] koukyuroku2008

    • Author(s)
      N.Kamiya
    • Journal Title

      RIMS 1604

      Pages: 110-114

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] koukyuroku2007

    • Author(s)
      N.Kamiya
    • Journal Title

      RIMS 1562

      Pages: 1-10

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exmples of Peirce deconyosition of triple systems2007

    • Author(s)
      N. Kamiya
    • Journal Title

      Alg, Gnoups and Geometry 24

      Pages: 325-348

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A geometuial characterization fnom triple systems2007

    • Author(s)
      N. Kamiya
    • Journal Title

      PADGE 2007

      Pages: 140-148

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On anti-structurable algebras and Dynkin diagrams

    • Author(s)
      N.Kamiya
    • Journal Title

      JGLTA vol.3 no 3

      Pages: 183-190

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Linear and Multilinear Algebras J.G. L.T.A (Sweden)

    • Author(s)
      神谷徳昭, 大久保進 ダニルモンドク 共著
    • Journal Title

      Bull.Aust.Math (印刷中)

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Presentation] (\alpha,\beta,\gamma)triple systems2011

    • Author(s)
      神谷徳昭
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      kyoto Univ
    • Related Report
      2010 Final Research Report
  • [Presentation] On anti-structurable algebras2010

    • Author(s)
      神谷徳昭
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      kyoto Univ
    • Related Report
      2010 Final Research Report
  • [Presentation] Triple systems and Lie algebras2010

    • Author(s)
      神谷徳昭
    • Organizer
      AGMP(ALGEBRA and Geometry,Math. Phy )6
    • Place of Presentation
      ヨーテボリ大学(スウェーデン)
    • Related Report
      2010 Final Research Report
  • [Presentation] Triple systems and Lie algebras2010

    • Author(s)
      神谷徳昭
    • Organizer
      AGMP 6 (Sweden)
    • Place of Presentation
      Sweden Goteborg Univ.
    • Related Report
      2010 Annual Research Report
  • [Presentation] 三項系代数学とリー代数の構成について研究発表3回2010

    • Organizer
      RIMS
    • Place of Presentation
      京都大
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] On (α,β,γ) title systems2010

    • Author(s)
      N.Ramiya
    • Organizer
      代数,言語・計算アルゴソズム
    • Place of Presentation
      京大
    • Related Report
      2009 Annual Research Report
  • [Presentation] パスカルの三角形と和算2009

    • Author(s)
      神谷徳昭
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大
    • Related Report
      2010 Final Research Report
  • [Presentation] パスカルの三角形と和算2009

    • Author(s)
      N.Kamiya
    • Organizer
      数学史の研究
    • Place of Presentation
      京大数理研
    • Related Report
      2008 Annual Research Report
  • [Presentation] 合成代数とピタゴラスの定理の拡張2008

    • Author(s)
      神谷徳昭
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大
    • Related Report
      2010 Final Research Report
  • [Presentation] 三項系代数学とリー代数の構成について研究発表3回2008

    • Organizer
      AGMF学会
    • Place of Presentation
      Sweden
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 三項系代数学とリー代数の構成について研究発表3回2008

    • Organizer
      NoMap学会
    • Place of Presentation
      Belugium
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 合成代数とピタゴラスの定理の拡張2008

    • Author(s)
      神谷 徳昭
    • Organizer
      京都大学数理研集会
    • Place of Presentation
      京都大学
    • Related Report
      2007 Annual Research Report
  • [Presentation] リー超代数とデインキン図形2007

    • Author(s)
      神谷徳昭
    • Organizer
      数理解析研究所研究集会
    • Place of Presentation
      京都大
    • Related Report
      2010 Final Research Report
  • [Presentation] 三項系とデインキン図形2007

    • Author(s)
      神谷徳昭
    • Organizer
      AGMP
    • Place of Presentation
      ヨーテボリ大学(スウェーデン
    • Related Report
      2010 Final Research Report
  • [Presentation] 三項系からの幾何学の特徴ずけについて

    • Author(s)
      神谷徳昭
    • Organizer
      Noncommutative Geometry Conference
    • Place of Presentation
      ベルギー
    • Related Report
      2010 Final Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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