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Study of infinite dimensional algebraic groups and Lie algebras, and applications to material science and life science

Research Project

Project/Area Number 19540006
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

MORITA Jun  University of Tsukuba, 大学院・数理物質科学研究科, 教授 (20166416)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords代数群 / リー環 / 物質科学 / 生命科学 / 群論 / カッツ・ムーディ群 / カッツ・ムーディ・リー環 / 単純群 / 局所アフィン・リー環 / ムーディ予想 / 準決勝 / 文字列 / DNA配列 / 単純性 / 双建物理論 / タイル張り / 双代数
Research Abstract

Some structures of infinite dimensional algebraic groups and Lie algebras have been studied. Especially, certain hyperbolic type Kac-Moody groups have been studied, and the classification of locally affine Lie algebras has been given. Algebraic theory related to finite and infinite sequences of letters has been created, and some algebraic method to control those sequences was found. Some useful mathematical applications to quasicrystals as material science and DNA sequences as life science have been constructed.

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

    (32 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (17 results) Remarks (2 results)

  • [Journal Article] Automorphisms and derivations of Borel subalgebras and theirnilradicals in Kac-Moody algebras2011

    • Author(s)
      Jun Morita, Kaiming Zhao
    • Journal Title

      Comm.Contemp.Math.

      Volume: (掲載確定)(未定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Tilings, Lie theory and combinatorics2010

    • Author(s)
      森田純
    • Journal Title

      Contemp.Math. 506

      Pages: 173-185

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Tilings, Lie theory and combinatorics2010

    • Author(s)
      Jun Morita
    • Journal Title

      Contemp. Math.(AMS) 506

      Pages: 173-185

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Tilings, Lie theory and combinatorics2010

    • Author(s)
      Jun Morita
    • Journal Title

      Contemp.Math.(AMS) 506

      Pages: 173-185

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Words, tilings and combinatorial spectra2009

    • Author(s)
      森田純, A.Terui
    • Journal Title

      Hiroshima Math.J. (1)39

      Pages: 37-60

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Words, tilings and combinatorial spectra2009

    • Author(s)
      Jun Morita, Akira Terui
    • Journal Title

      Hiroshima Math.J. (1)39

      Pages: 37-60

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Words, tilings and combinatorial spectra2009

    • Author(s)
      Jun Morita Akira Tarui
    • Journal Title

      Hiroshima Mathematical Journal 39

      Pages: 37-60

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Conjugacy results for the Lie algebra sl_2 over an algebra which is a UFD2007

    • Author(s)
      森田純, S.Berman
    • Journal Title

      Contemp.Math. 422

      Pages: 17-40

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new basis of U(sl_2) and Heisenberg analogue2007

    • Author(s)
      森田純, H.Chiba, J-L.Guo
    • Journal Title

      Hadronic J. 30

      Pages: 503-512

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A new basis of U(s1_2) and Heisenberg analogue2007

    • Author(s)
      Hideki Chiba, Jun Lin Guo, Jun Morita
    • Journal Title

      Hadronic J. 30

      Pages: 503-512

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Conjugacy results for the Lie algebra s1_2 over an algebra which is a UFD, Contemp2007

    • Author(s)
      Stephen Berman, Jun Morita
    • Journal Title

      Math. 422

      Pages: 17-40

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Conjugacy results for the Lie algebra sl_2 over an algebra which is a UFD2007

    • Author(s)
      Stephen Berman, Jun Morita.
    • Journal Title

      Contemp. Math. 422

      Pages: 17-40

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Automorphisms and derivations of Borel subalgebras and their nilradicals in Kac-Moody algebras

    • Author(s)
      森田純, K.Zhao
    • Journal Title

      Comm.Contemp.Math. 掲載許可済

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] Words, decomposition rules and invariants2010

    • Author(s)
      森田純
    • Organizer
      The mathematics of aperiodic orders, Korean Institute of Advanced Study
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2010 Final Research Report
  • [Presentation] Locally affine Lie algebras2010

    • Author(s)
      森田純
    • Organizer
      Workshop on QFT, string theory and mathematical physics
    • Place of Presentation
      北京、中華人民共和国(KITPC, Chinese Academy of Sciences)
    • Related Report
      2010 Final Research Report
  • [Presentation] 語・タイル張りの代数構造と組合せ構造2010

    • Author(s)
      森田純
    • Organizer
      代数と言語のアルゴリズムと計算理論
    • Place of Presentation
      京都大学、京都市
    • Related Report
      2010 Final Research Report
  • [Presentation] フィボナッチ数の数理2009

    • Author(s)
      森田純
    • Organizer
      数学教材研究会
    • Place of Presentation
      秋田工業高等専門学校、秋田市
    • Year and Date
      2009-03-19
    • Related Report
      2010 Final Research Report
  • [Presentation] 語・タイル張りに付随する代数的組合せ構造の具体的計算例2009

    • Author(s)
      森田純
    • Organizer
      高知タイル貼り小研究会
    • Place of Presentation
      高知大学、高知市
    • Related Report
      2010 Final Research Report
  • [Presentation] Algebraic approaches to words, tilings and quasicrystals2009

    • Author(s)
      森田純
    • Organizer
      Japan-Korea workshop on algebra and combinatorics
    • Place of Presentation
      九州大学、福岡市
    • Related Report
      2010 Final Research Report
  • [Presentation] 語、オートマトンおよび(リー)代数的不変量2009

    • Author(s)
      森田純
    • Organizer
      リー代数サマーセミナー
    • Place of Presentation
      九州工業大学、北九州市
    • Related Report
      2010 Final Research Report
  • [Presentation] Algebraic structures and combinatorics of words, and golden mean shifts2009

    • Author(s)
      森田純
    • Organizer
      準周期タイルと言語理論の周辺
    • Place of Presentation
      京大数理研、京都市
    • Related Report
      2010 Final Research Report
  • [Presentation] Moody's conjecture (II)2008

    • Author(s)
      Jun Morita
    • Organizer
      カナダ数学会
    • Place of Presentation
      カナダ国オタワ市(カールトン大学主催)
    • Year and Date
      2008-12-08
    • Related Report
      2008 Annual Research Report
  • [Presentation] Words, Tilings and Combinatorics2008

    • Author(s)
      Jun Morita
    • Organizer
      Quantum affine Lie algebras, extended affine Lie algebras, and applications
    • Place of Presentation
      Banff International Research Station, Canada
    • Year and Date
      2008-03-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Moody's conjecture2008

    • Author(s)
      森田純
    • Organizer
      Canadian Mathematical Society Winter Meeting
    • Place of Presentation
      Ottawa, Canada
    • Related Report
      2010 Final Research Report
  • [Presentation] Moody予想とその解決2008

    • Author(s)
      森田純
    • Organizer
      リー代数サマーセミナー
    • Place of Presentation
      福岡教育大学、宗像市
    • Related Report
      2010 Final Research Report
  • [Presentation] Words, tilings and combinatorics2008

    • Author(s)
      森田純
    • Organizer
      Workshop on quantum affine Lie algebras, extended affine Lie algebras and applications
    • Place of Presentation
      BIRS, Banff, Canada
    • Related Report
      2010 Final Research Report
  • [Presentation] Moody's conjecture, from derivations to automorphisms2008

    • Author(s)
      Jun Morita
    • Organizer
      カナダ数学会
    • Place of Presentation
      Ottawa (Canada)
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Group presentations, coverings and Schur multipliers in Lie theory2007

    • Author(s)
      Jun Morita.
    • Organizer
      Workshop on Algebraic Aspects of Lie Theory
    • Place of Presentation
      Academia Sinica, Taipei
    • Year and Date
      2007-12-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Group presentations, coverings and Schur multipliers in Lie theory2007

    • Author(s)
      森田純
    • Organizer
      Workshop on algebraic aspects of Lie theory
    • Place of Presentation
      Academia Sinica, Taipei, Taiwan
    • Related Report
      2010 Final Research Report
  • [Presentation] UFD上のリー代数と共役性定理2007

    • Author(s)
      森田純
    • Organizer
      リー代数サマーセミナー
    • Place of Presentation
      海上保安大学校、呉市
    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.math.tsukuba.ac.jp/~morita

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.math.tsukuba.ac.jp/~morita/

    • Related Report
      2009 Annual Research Report

URL: 

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

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