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Application of the non commutative Rokhlin property to Elliott classification problem

Research Project

Project/Area Number 20540220
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionRitsumeikan University

Principal Investigator

OSAKA Hiroyuki  Ritsumeikan University, 理工学部, 教授 (00244286)

Co-Investigator(Renkei-kenkyūsha) TERUYA Tamotsu  群馬大学, 教育学部, 准教授 (30594246)
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: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords作用素環 / C^*-環 / C^*-接合積 / ロホリン性 / 作用素環論 / C*-環論 / C*-指数理論 / Z-安定 / decomposition rank / nuclear dimension / Cuntz半群 / C*-環
Research Abstract

The Rokhlin property of an action from an amenable group on a C^*-algebra plays an important role in C^*-crossed product algebras when considering the Elliott classification problem in simple nuclear C^*-algebras.
We extended the Rokhlin property for a conditional expectation of a pair of C^*-algebras with a finite C^*-index. We obtained, then, several results about the transmission of important properties of C^*-algebras which play important roles in Elliott classification problem.

Report

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

    (41 results)

All 2011 2010 2009 2008 Other

All Journal Article (17 results) (of which Peer Reviewed: 16 results) Presentation (23 results) Remarks (1 results)

  • [Journal Article] Crossed products by finite group actions with the Rokhlin property2011

    • Author(s)
      H.Osaka, N.C.Phillips
    • Journal Title

      Math.Z. (印刷中 掲載確定 発行予定)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Note on the structure of matrix monotone functions, Frontiers of Analysis2011

    • Author(s)
      H.Osaka, J.Tomiyama
    • Journal Title

      Engineering Mathematics (印刷中 掲載確定 発行予定)

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Note on the structure of matrix monotone functions2011

    • Author(s)
      H.Osaka, J.Tmiyama
    • Journal Title

      Frontiers of Analysis, Engineering Mathematics

      Volume: (掲載決定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Operator convex functions on C^*-algebras2010

    • Author(s)
      H.Osaka, S.D.Silvestrov, J.Tomiyama
    • Journal Title

      the Proceedings of the Estonian Academy of Sciences 59巻

      Pages: 48-52

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Crossed products by finite group actions with the Rokhlin property2010

    • Author(s)
      H.Osaka, N.C.Phillips
    • Journal Title

      Math.Z. (掲載決定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Strongly self-absorbing property for inclusions of C^*-algebras with a finite Watatani index2010

    • Author(s)
      H.Osaka, T.Teruya
    • Journal Title

      arXiv.org(Mathematics)(プレプリントサーバー) 1002.4233

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Double piling structure of matrix monotone functions and of matrix convex functions2009

    • Author(s)
      H.Osaka, J.Tomiyama
    • Journal Title

      Linear and its Applications 431巻

      Pages: 1825-1832

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cancellation of C^*-crossed products2009

    • Author(s)
      J.A Jeong, H.Osaka, N.C.Phillips, T.Teruya
    • Journal Title

      Indiana J.Math. 58巻

      Pages: 1537-1564

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rohlin property for inclusions of C^*-algebras with a finite Watatani index2009

    • Author(s)
      K.Kodaka, H.Osaka, T.Teruya
    • Journal Title

      Contemporary Mathematics in Amer.Math.Soc. 503巻

      Pages: 179-195

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Operator convex functions on C^*-algebras2009

    • Author(s)
      H.Osaka, S.D.Silvestrov, J.Tomiyama
    • Journal Title

      the Proceedings of the Estonian Academy of Sciences 59

      Pages: 48-52

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Double piling structure of matrix monotone functions and of matrix convex functions2009

    • Author(s)
      H.Osaka, J.Tomiyama
    • Journal Title

      Linear and its Applications 431

      Pages: 1825-1832

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Cancellat ion of C*-crossed products2009

    • Author(s)
      J. A Jeong, H. Osaka, N. C. Phillips, T. Teruya
    • Journal Title

      Indiana J. Math. (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rohl in property for inclusions of C*-algebras with a finite Watatani index2009

    • Author(s)
      K. Kodaka, H. Osaka, T. Teruya
    • Journal Title

      Contemporary Mathematics in Amer. Math. Soc. (掲載決定)

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Rokhlin property for automorphisms on simple AT-algebras2008

    • Author(s)
      H.Lin, H.Osaka
    • Journal Title

      Ergod.Th.Dynam.Sys. 28巻

      Pages: 1215-1241

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stable rank for inclusions of C^*-algebras2008

    • Author(s)
      H.Osaka
    • Journal Title

      Internatinal Journal of Mathematics, 19巻

      Pages: 1011-1020

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Rokhlin property for automorphisms on simple AT-algebras2008

    • Author(s)
      H. Lin, H. Osaka
    • Journal Title

      Ergod. Th. Dynam. Sys. 28

      Pages: 1215-1241

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable rank for inclusions of C*-algebras2008

    • Author(s)
      H. Osaka
    • Journal Title

      Internatinal Journal of Mathematics 19

      Pages: 1011-1020

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Strongly self-absorbing property for inclusions of C^*-algebras with a finite Watatani index2011

    • Author(s)
      大坂博幸,照屋保
    • Organizer
      日本数学会2011年会
    • Place of Presentation
      早稲田大学理工学術院(東京都)
    • Year and Date
      2011-03-22
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Local property for C^*-algebras and the Rokhlin property2010

    • Author(s)
      大坂博幸,照屋保
    • Organizer
      作用素環論の最新の進展について
    • Place of Presentation
      京都大学数理解析研究所(京都府)
    • Year and Date
      2010-09-02
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Inclusion of unital C^*-algebras and the Rokhlin property2010

    • Author(s)
      大坂博幸
    • Organizer
      International Conference on Quantum Probability and Related Topics
    • Place of Presentation
      JNCASR (Bangalore, India)
    • Year and Date
      2010-08-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Inclusion of unital C^*-algebras and the Rokhlin property2010

    • Author(s)
      大坂博幸
    • Organizer
      International Conference on Quantum Probability and Related Topics
    • Place of Presentation
      JNCASR(Bangalore, India)
    • Year and Date
      2010-08-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Strongly self-absorbing property for inclusions of C^*-algebras with a finite Watatani index2010

    • Author(s)
      大坂博幸
    • Organizer
      Special Week on Operator Algebras
    • Place of Presentation
      East China Normal Univ. (Shanghai, China)
    • Year and Date
      2010-06-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Strongly self-absorbing property for inclusions of C^*-algebras with a finite Watatani index2010

    • Author(s)
      大坂博幸
    • Organizer
      Special Week on Operator Algebras
    • Place of Presentation
      East China Normal Univ.(Shanghai, China)
    • Year and Date
      2010-06-23
    • Related Report
      2010 Annual Research Report
  • [Presentation] Double piling structure of matrix monotone functions and of matrix convex functions2010

    • Author(s)
      大坂博幸
    • Organizer
      KOTAC2010
    • Place of Presentation
      Inchon大学(Seoul, Korea)
    • Year and Date
      2010-06-18
    • Related Report
      2010 Final Research Report
  • [Presentation] Double piling structure of matrix monotone functions and of matrix convex functions2010

    • Author(s)
      大坂博幸
    • Organizer
      KOTAC2010
    • Place of Presentation
      Inchon 大学(Seoul, Korea)
    • Year and Date
      2010-06-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Local properties for C^*-algebras and the Rokhlin property2009

    • Author(s)
      大坂博幸
    • Organizer
      2009 joint meeting of the Korean Mathematical Society and the American Mathematical Society
    • Place of Presentation
      Ehwa大学(Seoul, Korea)
    • Year and Date
      2009-12-17
    • Related Report
      2010 Final Research Report
  • [Presentation] The Rokhlin property for inclusions of C^*-algebras2009

    • Author(s)
      大坂博幸、小高一則、照屋保
    • Organizer
      日本数学会2009年度秋期総合分科会
    • Place of Presentation
      大阪大学(大阪府)
    • Year and Date
      2009-09-25
    • Related Report
      2010 Final Research Report 2009 Annual Research Report
  • [Presentation] Tracial approximation for crossed products by fnite groups with the tracial Rokhlin property2009

    • Author(s)
      大坂博幸
    • Organizer
      Special Week on Operator Algebras
    • Place of Presentation
      East China Normal Univ. (Shanghai, china)
    • Year and Date
      2009-06-23
    • Related Report
      2010 Final Research Report
  • [Presentation] Rokhlin property for inclusions of C^*-algebras with a finite Watatani index2009

    • Author(s)
      大坂博幸
    • Place of Presentation
      Kyungpook Univ (Daigo, Korea)
    • Year and Date
      2009-06-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Rokhlin property for inclusions of C^*-algebras with a finite Watatani index2009

    • Author(s)
      大坂博幸
    • Organizer
      KOTAC2009
    • Place of Presentation
      Kyungpook Univ(韓国)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Tracial approximation for crossed products by fnite groups with the tracial Rokhlin property2009

    • Author(s)
      大坂博幸
    • Organizer
      Special Week on Operator Algebras
    • Place of Presentation
      East China Normal University(中国)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Local properties for C^*-algebras and the Rokhlin property2009

    • Author(s)
      大坂博幸
    • Organizer
      2009 joint meeting of the Korean Mathematical Society and the American Mathematical Society
    • Place of Presentation
      Ehwa University(韓国)
    • Related Report
      2009 Annual Research Report
  • [Presentation] Cancellation for inclusions of C^*-algebras of finite depth2008

    • Author(s)
      J.A Jeong, 大坂博幸, 照屋保, N.C.Phillips
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学(東京都)
    • Year and Date
      2008-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Crossed products by finite group actions with the Rokhlin property2008

    • Author(s)
      大坂博幸, N.C.Phillips
    • Organizer
      日本数学会2008年度秋期総合分科会
    • Place of Presentation
      東京工業大学(東京都)
    • Year and Date
      2008-09-24
    • Related Report
      2010 Final Research Report
  • [Presentation] The Rokhlin property for inclusions of C^*-algebras with a finite Watatani index2008

    • Author(s)
      大坂博幸
    • Organizer
      Operator structures and Dynamical systems
    • Place of Presentation
      Leiden Univ. (Leiden, Nederland)
    • Year and Date
      2008-06-24
    • Related Report
      2010 Final Research Report
  • [Presentation] Stable rank for inclusions of C^*-algebras2008

    • Author(s)
      大坂博幸
    • Organizer
      KOTAC2008
    • Place of Presentation
      Seoul Univ. (Seoul, Korea)
    • Year and Date
      2008-06-20
    • Related Report
      2010 Final Research Report
  • [Presentation] Stable rank for inclusions of C*-algebras2008

    • Author(s)
      大坂博幸
    • Organizer
      KOTAC2008
    • Place of Presentation
      ソウル大学(韓国)
    • Related Report
      2008 Annual Research Report
  • [Presentation] The Rokhlin property for inclusions of C*-algebras with a finite Watatani index2008

    • Author(s)
      大坂博幸
    • Organizer
      Operator structures and Dynamical systems
    • Place of Presentation
      ライデン大学(オランダ)
    • Related Report
      2008 Annual Research Report
  • [Presentation] Crossed products by finite group actions with the Rokhlin property2008

    • Author(s)
      大坂博幸, N. C. Phillips
    • Organizer
      日本数学会2008年度秋期総合分科会, 日本数学会
    • Place of Presentation
      東京工業大学
    • Related Report
      2008 Annual Research Report
  • [Presentation] Cancellation for inclusions of C*-algebras of finite depth2008

    • Author(s)
      J. A Jeong, 大坂博幸, 照屋保, N. C. Phillips
    • Organizer
      日本数学会2008年度秋期総合分科会, 日本数学会
    • Place of Presentation
      東京工業大学
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.ritsumei.ac.jp/se/~osaka/

    • Related Report
      2010 Final Research Report

URL: 

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

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