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

Hopf-Galois theoretic approach to quantum groups

Research Project

Project/Area Number 20540036
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

MASUOKA Akira  University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (50229366)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsホップ代数 / 量子群 / スーパー群スキーム / ピカール・ヴェシオ理論 / 量子包絡環 / 群スキーム / ホップガロア理論 / コサイクル変形 / ホップガロア拡大 / 量子ダブル / ピカール・ウェシオ理論
Research Abstract

Hopf-Galois extensions of non-commutative algebras are a non-commutative analogue of principal homogeneous spaces(or torsors)in algebraic geometry, and of principal fiber bundles in algebraic topology. Ideas and techniques developed in Hopf-Galois theory can be effectively applied to study non-commutative or super-commutative algebras, and descent theory as well. The investigator did apply these to study quantum groups, algebraic super-groups and Picard-Vessiot theory. The obtained results include the construction of a series of Hopf algebras including the quantized enveloping algebras, by using cocycle deformation, together with its applications to study of generalized q-boson algebras and generalized quantum doubles.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (21 results)

All 2011 2010 2009 2008

All Journal Article (13 results) (of which Peer Reviewed: 12 results) Presentation (6 results) Book (2 results)

  • [Journal Article] Flatness and freeness properties of the generic Hopf Galois extensions2010

    • Author(s)
      C.Kassel, A.Masuoka
    • Journal Title

      Rev.Un.Mat.Argentina 51

      Pages: 79-94

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On minimal quasitriangular pointed Hopf algebras2010

    • Author(s)
      A.Masuoka
    • Journal Title

      J.Math.Sci.Univ.Tokyo 16

      Pages: 545-576

    • NAID

      120006906041

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On minimal quasitriangular pointed Hopf algebras2010

    • Author(s)
      Akira Masuoka
    • Journal Title

      J.Math.Sci.Univ.Tokyo

      Volume: 16 Pages: 545-576

    • NAID

      120006906041

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Flatness and freeness properties of the generic Hopf Galois extensions2010

    • Author(s)
      C.Kassel, A.Masuoka
    • Journal Title

      Rev Un.Mat.Argentina

      Volume: 51 Pages: 79-94

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized q-boson alge-bras and their integrable modules2009

    • Author(s)
      A.Masuoka
    • Journal Title

      J.Algebra 322

      Pages: 2199-2219

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semisimplicity criteria for irreducible Hopf algebras2009

    • Author(s)
      A.Masuoka
    • Journal Title

      Proc.Amer.Math.Soc. 137

      Pages: 1925-1932

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semisimplicity criteria for irreducible Hopf algebras in positive characteristic2009

    • Author(s)
      増岡彰(Akira Masuoka)
    • Journal Title

      Proceeding of the American Mathematical Society 137

      Pages: 1925-1932

    • NAID

      120007138357

    • Related Report
      2009 Annual Research Report 2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized q-boson algebras and their integrable modules2009

    • Author(s)
      増岡彰(Akira Masuoka)
    • Journal Title

      Journal of Algebra 322

      Pages: 2199-2219

    • NAID

      120007131509

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article]2009

    • Author(s)
      天野勝利、増岡彰、竹内光弘
    • Journal Title

      Handbook of Algebra Vol.6(分担執筆Hopf algebraic Approach to Picard-Vessiot Theoryの章)(Elsevier/North-Holland)

      Pages: 127-171

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Construction of quantized enveloping algebras by cocycle deformation2008

    • Author(s)
      A.Masuoka
    • Journal Title

      Arab.J.Sci.Eng.Sect.C Theme Issues 33

      Pages: 387-406

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Abelian and non-abelian second cohomologies for quantized enveloping algebras2008

    • Author(s)
      A.Masuoka
    • Journal Title

      J.Algebra 320

      Pages: 1-47

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Abelian and non-abeiian second cohomologies of quantized enveloping algebras2008

    • Author(s)
      増岡彰(Akira Masuoka)
    • Journal Title

      Journal of Algebra 320

      Pages: 1-47

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Construction of quantized enveloping algebras by cocycle deformation2008

    • Author(s)
      増岡彰(Akira Masuoka)
    • Journal Title

      The Arabian Journal for Science and Engineering 33-2C

      Pages: 387-406

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Hopf algebraic approach to Picard-Vessiot theory2011

    • Author(s)
      A.Masuoka
    • Organizer
      AMS-MAA合同数学会議
    • Place of Presentation
      ニューオリオンズ(米国)
    • Year and Date
      2011-01-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Hopf algebraic approach to Picard-Vessiot theory2010

    • Author(s)
      A.Masuoka
    • Organizer
      Galois Theory and Explicit Methods
    • Place of Presentation
      スペイン・バルセロナ大学
    • Year and Date
      2010-09-07
    • Related Report
      2010 Final Research Report
  • [Presentation] Hopf Galois approach to Picard-Vessiot theory2010

    • Author(s)
      Akira Masuoka
    • Organizer
      Galois theory and explicit methods
    • Place of Presentation
      スペイン・バルセロナ大学(招待講演)
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report
  • [Presentation] On affine super groups2010

    • Author(s)
      A.Masuoka
    • Organizer
      Non-commutative Algebras and Quantum Groups, Conference in Honor of Prof. Mia Cohen
    • Place of Presentation
      イスラエル・Ben Gurion大学
    • Year and Date
      2010-05-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Hopf-Galois approach to quantum groups2009

    • Author(s)
      A.Masuoka
    • Organizer
      Conference in Honor of Prof. Hans-Juergen Schneider
    • Place of Presentation
      アルゼンチン国立コルドバ大学
    • Year and Date
      2009-09-05
    • Related Report
      2010 Final Research Report
  • [Presentation] Hopf-Galois approach to quantum groups2009

    • Author(s)
      増岡彰(Akira Masuoka)
    • Organizer
      Conference in honor of Professor Hans-Juergen Schneider
    • Place of Presentation
      アルゼンチン、コルドバ
    • Year and Date
      2009-09-05
    • Related Report
      2009 Annual Research Report
  • [Book] Handbook of Algebra(Classification of semisimple Hopf algebras)(M.Hazewinkel ed.) Vol.62009

    • Author(s)
      K.Amano, A.Masuoka, M.Takeuchi
    • Publisher
      Elsevier(分担執筆)
    • Related Report
      2010 Final Research Report
  • [Book] Handbook of Algebra(Classification of semisimple Hopf algebras)(M.Hazewinkel ed.) Vol.52008

    • Author(s)
      A.Masuoka
    • Publisher
      Elsevier(分担執筆)
    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi