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Research of automorphism groups and group action classification of operator algebras

Research Project

Project/Area Number 23540246
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionKyushu University

Principal Investigator

Masuda Toshihiko  九州大学, 数理(科)学研究科(研究院), 准教授 (60314978)

Co-Investigator(Renkei-kenkyūsha) Tomatsu Reiji  北海道大学, 理学研究科, 准教授 (70447366)
Project Period (FY) 2011-04-28 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords作用素環 / 群作用 / 一径数自己同型群 / 離散従順群 / コンパクト群 / 自己同型 / 部分因子環 / テンソル圏 / 分類 / von Neumann環 / ロホリン性 / 単射的因子環
Outline of Final Research Achievements

| mainly study group actions on operator algebras. As a results, I first obtained a unified proof of classification theorem of discrete amenable group actions on injective factors. Next, I classified one-parameter automorphism groups with Rohlin property with Reiji Tomatsu. As one application, we present a proof of uniqueness of the injective factor of type III_1 from point of view of structure theorem of factors. I also study classification of compact group actions on injective factors with Reiji Tomatsu. In particular, we obtained classification theorem of actions of groups with nice topological property, e.g., compact Lie groups.

Report

(6 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (14 results)

All 2016 2015 2014 2013 2012 2011

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 4 results) Presentation (9 results)

  • [Journal Article] Rohlin flows on von Neumann algebras2016

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

      Memoirs of the American Mathematical Society

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Classification of actions of discrete Kac algebras on injective factors2016

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

      Memoirs of the American Mathematical Society

      Volume: 未定

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Rohlin flow on von Neumann algebras2015

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

      Memoirs of the American Mathematical Society

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Classification of actions of discrete Kac algebras on injective factors2015

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

      Memoirs of the American Mathematical Society

      Volume: 未定

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Unified approach to classification of discrete amenable groups on injective factors2013

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Journal fur die Reine und angewandte Mathematik

      Volume: 印刷中 Issue: 683 Pages: 1-47

    • DOI

      10.1515/crelle-2011-0011

    • Related Report
      2013 Research-status Report 2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 離散従順群の単射的因子環への外部的作用(G-kernel)の分類について2015

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] Connes の単射的III1 型因子環の分類についての議論の紹介と補足(モジュラー自己同型の近似的内部性について)2015

    • Author(s)
      増田俊彦
    • Organizer
      RIMS 共同研究「作用素環の分類理論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-02-02 – 2015-02-04
    • Related Report
      2014 Research-status Report
  • [Presentation] Braided system上のgradingとLongo-Rehren inclusion2014

    • Author(s)
      増田俊彦
    • Organizer
      作用素環論とその周辺理論の発展
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2013 Research-status Report
  • [Presentation] Classification of group actions on von Neumann algebras2013

    • Author(s)
      増田俊彦
    • Organizer
      Workshop on Operator Algebras ― for the 80th birthday of Masamichi Takesaki
    • Place of Presentation
      東京大学
    • Related Report
      2013 Research-status Report
  • [Presentation] フォンノイマン環上のロホリン的な流れの分類について2013

    • Author(s)
      増田俊彦
    • Organizer
      第52回実函数論函数解析合同シンポジウム
    • Place of Presentation
      青山学院大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Orbifold構成法での障害が消えるための十分条件2013

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Classification of group actions on von Neumann algebras2013

    • Author(s)
      Toshihiko Masuda
    • Organizer
      Workshop on Operator algebras
    • Place of Presentation
      東京大学数理科学研究院
    • Related Report
      2012 Research-status Report
  • [Presentation] Rohlin flows on injective factors2012

    • Author(s)
      Toshihiko Masuda
    • Organizer
      Conference on von Neumann Algebras and Related Topics(招待講演)
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2011 Research-status Report
  • [Presentation] Rohlin flows on injective factors2011

    • Author(s)
      増田俊彦
    • Organizer
      作用素論作用素環論研究会
    • Place of Presentation
      琉球大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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