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Research of symmetries arising from automorphisms of operator algebras

Research Project

Project/Area Number 16K05180
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Masuda Toshihiko  九州大学, 数理学研究院, 教授 (60314978)

Project Period (FY) 2016-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords因子環 / 自己同型群 / 対称性 / 群作用 / 作用素環 / エルゴード理論 / エルゴート変換 / 充足群 / 離散従順亜群 / テンソル圏 / 部分因子環 / 離散亜群 / 流れ / 再中心化環 / C*テンソル圏 / Q-system / 自己同型
Outline of Final Research Achievements

I studied the symmetries of operator algebras by focusing on automorphism groups of operator algebras. I obtained the following results mainly. 1. Classification of Roberts actions of tensor categories on the injective type III_1 factor. 2. I solved the conjecture of Ando-Haagerup-Houdayer-Marakech about the flows of relative bicentralizer associated with inclusion of type III_1 factors when small algebra is injective. 3. I classified outer actions (G-kernels) of discrete amenable groupoids on injective factors. My proof does not require the method of model actions to get rid of obstraction, and it is more natural. 4. I classified actions of discrete amenable groups on orbit equivalence of ergodic theory.

Academic Significance and Societal Importance of the Research Achievements

私の研究によって、作用素環の群作用や自己同型群の対称性の理解がより深まった。特にテンソル圏との関連において深い理解が得られたと考える。またエルゴード理論のように作用素環と関連する分野においても、作用素環論に由来するアイディアが有効に使えることも明確となり、理論の発展に大きく寄与した。

Report

(8 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (18 results)

All 2023 2022 2021 2020 2019 2018 2017 2016

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 7 results,  Acknowledgement Compliant: 3 results) Presentation (11 results)

  • [Journal Article] Classification of outer actions of discrete amenable groupoids on injective factors2022

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 74 Issue: 3 Pages: 873-901

    • DOI

      10.2969/jmsj/86328632

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2022 Annual Research Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III_12020

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Publications of the Research Institute for Mathematical Sciences

      Volume: 56 Issue: 2 Pages: 391-400

    • DOI

      10.4171/prims/56-2-4

    • Related Report
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A simple sufficient condition for triviality of obstructions in the orbifold construction for subfactors2017

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      Mathmatica Scandinavia

      Volume: 121 Issue: 1 Pages: 101-110

    • DOI

      10.7146/math.scand.a-26240

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Classification of Roberts actions of strongly amenable C*tensor categories on the injective factor of type III_12017

    • Author(s)
      Toshihiko Masuda
    • Journal Title

      International Journal of Mathematics

      Volume: 28 Issue: 07 Pages: 1750002-1750002

    • DOI

      10.1142/s0129167x17500525

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A simple sufficient condition for triviality of obstruction in the orbifold construction for subfactors2017

    • Author(s)
      T. Masuda
    • Journal Title

      Mathematica Scandinavica

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Rohlin flows on von Neumann algebras2016

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

      Memoirs of the American Mathematical Society

      Volume: 244 Issue: 1153 Pages: 0-0

    • DOI

      10.1090/memo/1153

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Classification of actions of discrete Kac algebras on injective factors2016

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

      Memoirs of the American Mathematical Society

      Volume: 245 Issue: 1160 Pages: 0-0

    • DOI

      10.1090/memo/1160

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Actions of discrete amenable groups into the normalizers of full groups of ergodic transformations2023

    • Author(s)
      Toshihiko Masuda
    • Organizer
      RIMS 共同研究プログラム 「作用素環論における群作用と数理物理の関連」
    • Related Report
      2022 Annual Research Report
  • [Presentation] Classification of outer actions of discrete amenable groupoids on injective factors2021

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] Classification of outer actions of discrete amenable groupoids on injective factors2021

    • Author(s)
      増田俊彦
    • Organizer
      研究集会「作用素環論の最近の進展」
    • Related Report
      2021 Research-status Report
  • [Presentation] Outer actions (G-kernels) of discrete amenable groupoids on injective factors2020

    • Author(s)
      増田俊彦
    • Organizer
      東大京大合同オンライン作用素環セミナー
    • Related Report
      2020 Research-status Report
  • [Presentation] On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III_12019

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会
    • Related Report
      2019 Research-status Report
  • [Presentation] On the relative bicentralizer flows and the relative flow of weights of inclusions of factors of type III_12019

    • Author(s)
      増田俊彦
    • Organizer
      作用素論作用素環研究集会
    • Related Report
      2019 Research-status Report
  • [Presentation] Tannaka-Krein-Woronowicz duality from the viewpoint of Q-systems,2018

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] 強従順なC^*テンソル圏のロバーツ作用の分類について2017

    • Author(s)
      増田俊彦
    • Organizer
      日本数学会函数解析分科会
    • Place of Presentation
      首都大学東京
    • Year and Date
      2017-03-26
    • Related Report
      2016 Research-status Report
  • [Presentation] Classification of Roberts actions of strongly amenable C*-tensor categories on the injective factor of type III_12017

    • Author(s)
      増田俊彦
    • Organizer
      東大作用素環セミナー
    • Related Report
      2017 Research-status Report 2016 Research-status Report
  • [Presentation] 冨田竹崎理論の紹介とそれに関連する話題2017

    • Author(s)
      増田俊彦
    • Organizer
      第56回実函数函数解析合同シンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] 強従順なC^*テンソル圏のロバーツ作用の分類について2016

    • Author(s)
      増田俊彦
    • Organizer
      作用素環論エルゴート理論セミナー
    • Place of Presentation
      九州大学
    • Year and Date
      2016-10-17
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2024-01-30  

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