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Actions of discrete groups on operator algebras and their invariants

Research Project

Project/Area Number 21740119
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Global analysis
Research InstitutionOsaka Kyoiku University

Principal Investigator

OKAYASU Rui  大阪教育大学, 教育学部, 准教授 (70362746)

Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords作用素環 / エントロピー / 離散群 / 自己同型写像 / 自由群 / 郡環 / 従順性 / 群作用 / C*-環 / von Neumann環
Research Abstract

I study some entropy on operator algebras.(1) By using the method of Voiculescu, I define new entropy for an autromorphism on a TAF algebra, which is defined by Lin, and study their properties and examples.(2) I study the relative entropy for a pair of an operator algebra and a subalgebra, which is defined by Pimsner and Popa. I also study the relative entropy for a pair of two subalgebras, which is defined by M. Choda.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (21 results)

All 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (14 results) Remarks (2 results)

  • [Journal Article] Entropy for C*-algebras with tracial rank zero2010

    • Author(s)
      Rui Okayasu
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 138 Pages: 3609-3621

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative entropy for abelian subalgebras2010

    • Author(s)
      Rui Okayasu:
    • Journal Title

      International Journal of Mathematics

      Volume: 21 Pages: 537-550

    • Related Report
      2012 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for C^*-algebras with tracial rank zero2010

    • Author(s)
      Rui Okayasu
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 138 Pages: 3609-3621

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Entropy for C^*-algebras with tracial rank zero

    • Author(s)
      Rui Okayasu
    • Journal Title

      Proceedings of the American Mathematical Society (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relative entropy for abelian subalgebras

    • Author(s)
      Rui Okayasu
    • Journal Title

      International Journal of Mathematics (印刷中)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      京都作用素環セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      Great Plains Operator Theory Symposium
    • Place of Presentation
      University of HoustonHouston(アメリカ合衆国)
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      Workshop on Semiprojective C*-Algebras
    • Place of Presentation
      University of Copenhagen(デンマーク)
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      日本数学会函数解析学分科会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      研究集会「作用素環論の最近の発展と関連する話題について」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with lp2012

    • Organizer
      Harmonic analysis, operator algebras and representations
    • Place of Presentation
      CIRM(フランス)
    • Related Report
      2012 Final Research Report
  • [Presentation] Free group C*-algebras associated with l_p2012

    • Author(s)
      岡安類
    • Organizer
      GPOTS2012
    • Place of Presentation
      University of Houston (アメリカ)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Free group C*-algebras associated with l_p2012

    • Author(s)
      岡安類
    • Organizer
      Workshop on Semiprojective C*-Algebras
    • Place of Presentation
      University of Copenhagen (デンマーク)
    • Related Report
      2012 Annual Research Report
  • [Presentation] Free group C*-algebras associated with l_p2012

    • Author(s)
      岡安類
    • Organizer
      日本数学会
    • Place of Presentation
      九州大学
    • Related Report
      2012 Annual Research Report
  • [Presentation] Free group C*-algebras associated with l_p2012

    • Author(s)
      岡安類
    • Organizer
      RIMS研究集会
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Free group C*-algebras associated with l_p2012

    • Author(s)
      岡安類
    • Organizer
      Harmonic analysis, operator algebras and representations
    • Place of Presentation
      CIRM(フランス)
    • Related Report
      2012 Annual Research Report
  • [Presentation] On the Toeplitz algebras of quasi-lattice ordered groups2011

    • Organizer
      共同研究「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
      2012 Final Research Report
  • [Presentation] Entropy for C*-algebras with tracial rank zero2010

    • Organizer
      日本数学会函数解析学分科会
    • Place of Presentation
      名古屋大学
    • Related Report
      2012 Final Research Report
  • [Presentation] Tracial topological approximation entropy2010

    • Organizer
      作用素論・作用素環論研究集会
    • Place of Presentation
      東京理科大学森戸記念館
    • Related Report
      2012 Final Research Report
  • [Remarks]

    • URL

      http://www.osaka-kyoiku.ac.jp/~rui/index-j.html

    • Related Report
      2012 Final Research Report
  • [Remarks] 岡安類のホームページ

    • URL

      http://www.osaka-kyoiku.ac.jp/~rui/index-j.html

    • Related Report
      2012 Annual Research Report

URL: 

Published: 2009-04-01   Modified: 2019-07-29  

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