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A research on algebraic groups and Kac-Moody groups, and their applications

Research Project

Project/Area Number 15540005
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, Graduate School of Pure and Applied Science, Professor, 大学院数理物質科学研究科, 教授 (20166416)

Project Period (FY) 2003 – 2006
Project Status Completed (Fiscal Year 2006)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsalgebraic groups / quantum group / integrability / tiling / extended affine Lie algebra / Kac conmiecture / combinatorics / conjugacy theorem / Kac-Moody theory / extended affine Lie algebra / 代数群 / kac-Moody群 / 拡大アフィンLie代数 / 局所拡大アフィンLie代数 / 準結晶 / タイル張り / 一意分解環 / Gauss分解 / リー代数 / ルート系 / Bruhat分解 / Kac-Moody群 / フィボナッチ数列
Research Abstract

(1) We introduced a new formulas for U q(sl_2), and gave a sufficient condition for its representation to be integrable.
(2) We gave a proof of the so-called Kac-conjecture for extended affine Lie algebras.
(3) We introduced certain bialgebras associated with given one-dimensional tilings, and gave a characterization for such tilings to be locally indistinguishable using our bialgebras.
(4) We constructed universal central extensions of certain adjoint groups associated with completed extended affine Lie algebras with nullity 2.
(5) We showed the fact that the groups and Lie algebras defined by one-dimensional tilings have standard and additive Gauss decompositions.
(6) We proved many conjugacy theorems for sl_2 of UFD algebras over fields, especially for Cartan subalgebras and for TDS as some analogue of Jacobson-Morozov theorem.

Report

(5 results)
  • 2006 Annual Research Report   Final Research Report Summary
  • 2005 Annual Research Report
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • Research Products

    (11 results)

All 2006 2004 2003 Other

All Journal Article (10 results) Publications (1 results)

  • [Journal Article] Locally extended affine Lie algebras2006

    • Author(s)
      Jun Morita
    • Journal Title

      Journal of Algebra 301・1

      Pages: 59-81

    • NAID

      120007131213

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Groups, Lie algebras and Gauss decompositions for one dimensional tilings2006

    • Author(s)
      Daisuke Dobashi
    • Journal Title

      Nihonkai Mathematical Journal 17・1

      Pages: 77-88

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Groups defined by extended affine Lie algebras with nullity 22006

    • Author(s)
      Jun Morita
    • Journal Title

      Tokyo Journal of Mathematics 29・2

      Pages: 347-383

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Annual Research Report 2006 Final Research Report Summary
  • [Journal Article] Locally extended affine Lie algebras2006

    • Author(s)
      Jun, Morita
    • Journal Title

      Journal of Algebra 301(1)

      Pages: 59-81

    • NAID

      120007131213

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Groups, Lie algebras and Gauss decompositions for one dimensional tilings2006

    • Author(s)
      Daisuke, Dobashi
    • Journal Title

      Nihonkai Mathematical Journal 17(1)

      Pages: 77-88

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Groups defined by extended affine Lie algebras with nullity 22006

    • Author(s)
      Jun, Morita
    • Journal Title

      Tokyo Journal of Mathematics 29(2)

      Pages: 347-383

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Local properties, bialgebras and representations for one-dimensional tilings2004

    • Author(s)
      Takashi Masuda
    • Journal Title

      Journal of Physics A : Mathematics General 37

      Pages: 2661-2669

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Local properties, bialgebras and representations for one-dimensional tilings2004

    • Author(s)
      Takashi, Masuda
    • Journal Title

      Journal of Physics A Mathematics General 37

      Pages: 2661-2669

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some formulae in $U_q(s1_2)$ and diagonalizability2003

    • Author(s)
      Jun Morita
    • Journal Title

      Kyushu Journal of Mathematics 57・1

      Pages: 165-173

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Journal Article] Some formulae in $U_q(sl_2)$ and diagonalizability2003

    • Author(s)
      Jun, Morita
    • Journal Title

      Kyushu Journal of Mathematics 57(1)

      Pages: 165-173

    • NAID

      120000981331

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2006 Final Research Report Summary
  • [Publications] Takashi Masuda, Jun Morita: "Local properties, bialgebras and representations for one dimensional tilings"J.Phys.A Math.Gen.. 37. 2661-2669 (2004)

    • Related Report
      2003 Annual Research Report

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Published: 2003-04-01   Modified: 2016-04-21  

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