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Research of automorphism groups and group actions in the Theory of operator algebras

Research Project

Project/Area Number 19740088
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionKyushu University

Principal Investigator

MASUDA Toshihiko  Kyushu University, 数理学研究院, 准教授 (60314978)

Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,630,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
Keywords単射的因子環 / 自己同型群 / 群作用 / 分類 / コンパクト群 / 作用素環 / 離散従順群 / 単射的III型因子環 / コンパクトカッツ環 / 極小作用 / 2次コサイクル / コンバクトカッツ環 / 自己準同型
Research Abstract

I studied automorphism groups and group actions on injective factors. In particular, I studued classificatgion theory of amenable group actions on injective factors. With R.Tomatsu, I classified actions of discrete amenable Kac algebras, and minimal actions of compact groups on injective factors through the duality theorem. I also found a unified proof of classification of discrete amenable group actions on injective factors by Evans-Kishimoto's intertwining argument. By generalizing this argument, I also gave the classification of discrete amenable group actions on subfactors, and outer actions of discrete amenable groups on injective factors.

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

    (25 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 11 results) Presentation (11 results) Remarks (1 results)

  • [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III2010

    • Author(s)
      Toshihiko Masuda, Reiji Tomatsu
    • Journal Title

      Journal of Functional Analysis 258

      Pages: 1965-2025

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual on injective factors of type III2010

    • Author(s)
      T.Masuda, R, Tomatsu
    • Journal Title

      Journal of functional analysis

      Volume: 258 Pages: 1965-2025

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of actions of minimal actions of a compact Kac algebra with amenable dual on infective factors of type III2010

    • Author(s)
      T.Masuda, R.Tomatsu
    • Journal Title

      Journal of Functional Analysis 258

      Pages: 1965-2025

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximate innerness and central triviality of endomorphisms2009

    • Author(s)
      Toshihiko Masuda, Reiji Tomatsu
    • Journal Title

      Advance in Mathematics 220

      Pages: 1075-1134

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Approximate innerness and central triviality of endomorphisms2009

    • Author(s)
      T. Masuda and R. Tomatsu
    • Journal Title

      Advance in Mathematics 220

      Pages: 1075-1134

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of actions of duals of finite groups on the AFD factor of type II_12008

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Journal of Operator Theory 60

      Pages: 273-300

    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Classification of actions of duals of finite groups on the AFD factor of type II_12008

    • Author(s)
      T. Masuda
    • Journal Title

      Journal of Operator theory 60

      Pages: 273-300

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Evans-Kishimoto type argument for actions of discrete amenable groups on McDuff factors2007

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Mathematica.Scandinavia 101

      Pages: 48-64

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual2007

    • Author(s)
      Toshihiko Masuda, Reiji Tomatsu
    • Journal Title

      Commucations in Mathematical Physics. 274

      Pages: 487-551

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual2007

    • Author(s)
      Toshihiko Masuda, Reiji Tomatsu
    • Journal Title

      Commucations in Mathematical Physics 274

      Pages: 487-551

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] ishimoto type argument for actions of discrete amenable groups on McDuff factors, Mathematica.2007

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Scandinavia 101

      Pages: 48-64

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] Classification of minimal actions of a compact Kac algebra with amenable dual2007

    • Author(s)
      T., Masuda・R., Tomatsu
    • Journal Title

      Communications in Mathematical Physics 274

      Pages: 487-551

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Evans-Kishimoto type intertwining argument for McDuff factors2007

    • Author(s)
      T., Masuda
    • Journal Title

      Mathematica Scandinavia 101

      Pages: 48-64

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] フォンノイマン環への群・量子群作用の分類2011

    • Author(s)
      増田俊彦
    • Organizer
      研究集会 作用素環の対称性の研究
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Final Research Report
  • [Presentation] フォンノイマン環への群・量子群作用の分類2011

    • Author(s)
      増田俊彦
    • Organizer
      研究集会「作用素環論の対称性の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2010 Annual Research Report
  • [Presentation] 離散従順群の単射的因子環へのモデル作用の構成について2010

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Evans-岸本型のintertwiningargumentの一般化と離散従順群の単射的因子環への作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Evans-岸本型のintertwining argumentの一般化と離散従順群の単射的因子環への作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Evans-岸本型のintertwining argumentの一般化と離散従順群の単射的因子環への作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会
    • Place of Presentation
      大阪大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Evans-Kishimoto intertwiningargumentの一般化による単射的因子環への離散従順群の作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      研究集会 作用素環論とその関連分野の研究
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Evans-Kishimoto intertwining argumentの一般化による単射的因子環への離散従順群の作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      研究集会「作用素環論とその関連分野の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-09-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] Evans-Kishimoto intertwining argumentの一般化による単射的因子環への離散従順群の作用の分類2009

    • Author(s)
      増田俊彦
    • Organizer
      研究集会「作用素環論とその関連分野の研究」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-09-03
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Classification of minimal actions of a compact Kac algebra with amenable dual2007

    • Author(s)
      Toshihiko Masuda
    • Organizer
      Operator algebra seminars
    • Place of Presentation
      Fields institute
    • Year and Date
      2007-11-29
    • Related Report
      2010 Final Research Report 2009 Self-evaluation Report
  • [Presentation] Classificlam of mmmlaclms for compuct kac algelm on the awarable 〓2007

    • Author(s)
      T., Masuia
    • Organizer
      Operator Algelm Seminar
    • Place of Presentation
      フィールズ研究所
    • Year and Date
      2007-11-27
    • Related Report
      2007 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www2.math.kyushu-u.ac.jp/~masuda

    • Related Report
      2010 Final Research Report

URL: 

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

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