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C*-algebras and its applications to classification of symbolic dynamical systems and study of orbit equivalence

Research Project

Project/Area Number 15K04896
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionJoetsu University of Education

Principal Investigator

Matsumoto Kengo  上越教育大学, 大学院学校教育研究科, 教授 (40241864)

Project Period (FY) 2015-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords記号力学系 / C*環 / 位相的マルコフシフト / 軌道同型 / 位相共役 / 双曲型力学系 / flow equivalence / Cutz-Krieger 環 / C*-環 / 作用素環 / サブシフト / Cuntz-Krieger algebra / Ruelle algebra / C*環 / スメール空間 / 軌道同値 / Cuntz-Krieger 環 / C*環 / 強シフト同値 / Ruelle 環
Outline of Final Research Achievements

I have been studying classification of symbolic dynamics and orbit equivalence through isomorphism class of their related C*-algebras and their gauge actions.
As a result, I have been able to publish 21 research papers in internal research journals. I have found, as main results, that there are interesting relation ship among classifications of one-sided topological Markov shifts under topological conjugacy, orbit equivalence , flow equivalence
and gage actions on the associated C*-algebras. Furthermore I have extended these classifications to general symbolic dynamics and Smale spaces in hyperbolic dynamical systems. The technique is mainly groupoids constructed from the dynamical systems.

Academic Significance and Societal Importance of the Research Achievements

記号力学系は、一般の力学系の最も基礎的であり、かつ大事な位相力学系のクラスであり、この力学系のさまざまな意味での分類は、一般の力学系の種々の分類に起因してなされるべき、数学的に興味深い研究対象である。また一方作用素環、特にC*-環の分類は量子力学の物理量のなす代数系と考えられ、量子化された枠組みを扱う数学であるといえる。
この二つの一見相異なる数学的対象に密接な関係があり、特に互いにその分類や構成に、そのもだけを見ていては見えなかった重要な要因を与えている。本研究では、このように力学系とC*-環という二つの数学的対象に、それぞれの分類を通して、互いに密接な関係があることを見出したものである。

Report

(6 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (35 results)

All 2020 2019 2018 2017 2016 2015 Other

All Int'l Joint Research (4 results) Journal Article (23 results) (of which Int'l Joint Research: 16 results,  Peer Reviewed: 22 results,  Open Access: 17 results,  Acknowledgement Compliant: 6 results) Presentation (8 results)

  • [Int'l Joint Research] ハイデルベルグ大学(ドイツ)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Heidelberg University(Germany)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] Heidelberg University(Germany)

    • Related Report
      2016 Research-status Report
  • [Int'l Joint Research] Heidelberg University(Germany)

    • Related Report
      2015 Research-status Report
  • [Journal Article] Subshifts, lambda-graph-bisystems and C*-algebras2020

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 485 Issue: 2 Pages: 123843-123843

    • DOI

      10.1016/j.jmaa.2020.123843

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A groupoid approach to C*-algebras associated with lambda-graph systems and continuous orbit equivalence of subshifts2020

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Dynamical Systems

      Volume: - Issue: 3 Pages: 398-429

    • DOI

      10.1080/14689367.2020.1716952

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Continuous orbit equivalence of Markov shifts and KMS states on Cuntz-Krieger algebras2020

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: -

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] State splitting, strong shift equivalence and stable isomorphism of Cuntz-Krieger algebras2019

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Dynamical Systems

      Volume: 34 Issue: 1 Pages: 93-112

    • DOI

      10.1080/14689367.2018.1470227

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Markov-Dyck shifts, neutral periodic points and topological conjugacy2019

    • Author(s)
      Wolfgang Krieger and Kengo Matsumoto
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: 39 Issue: 1 Pages: 1-18

    • DOI

      10.3934/dcds.2019001

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Asymptotic continuous orbit equivalence of Smale spaces and Ruelle algebras2019

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 71 Pages: 1243-1296

    • Related Report
      2019 Annual Research Report 2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Topological Conjugacy of topological Markov shifts and Ruelle algebras2019

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Journal of Operator Theory

      Volume: 82 Issue: 2 Pages: 253-284

    • DOI

      10.7900/jot.2018apr08.2235

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] A short note on Cuntz splice from a viewpoint of continuous orbit equivalence of topological Markov shifts2018

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Mathematica Scandinavica

      Volume: 123 Issue: 1 Pages: 91-100

    • DOI

      10.7146/math.scand.a-102939

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Relative Morita equivalence of Cuntz-Krieger algebras and flow equivalence of topological Markov shifts2018

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 370 Issue: 10 Pages: 7011-7050

    • DOI

      10.1090/tran/7272

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Imprimitivity bimodules of Cuntz-Krieger algebras and strong shift equivalences of matrices2018

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Dynamical Systems

      Volume: 33 Issue: 2 Pages: 253-274

    • DOI

      10.1080/14689367.2017.1351922

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] K-theory for the simple C*-algebra of the Fibonacci-Dyck shift2017

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Acta Scientiarum Mathematicarum

      Volume: 83 Issue: 1-2 Pages: 177-200

    • DOI

      10.14232/actasm-015-323-0

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On extensions of subshifts by finite groups2017

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Dynamical Systems

      Volume: 32 Issue: 3 Pages: 423-459

    • DOI

      10.1080/14689367.2016.1278430

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Full groups of Cuntz-Krieger algebras and Higman-Thompson groups2017

    • Author(s)
      Kengo Matsumoto and Hiroki Matui
    • Journal Title

      Groups, Geometry, and Dynamics

      Volume: 11 Issue: 2 Pages: 499-531

    • DOI

      10.4171/ggd/405

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Topological conjugacy of topological Markov shifts and Cuntz-Krieger algebras2017

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Documenta Mathematica

      Volume: 22 Pages: 873-915

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Continuous orbit equivalence, flow equivalence of Markov shifts and circle actions on Cuntz-Krieger algebras.2017

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Mathematische Zeitschrift

      Volume: 285 Issue: 1-2 Pages: 121-141

    • DOI

      10.1007/s00209-016-1700-3

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz-Krieger algebras.2017

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 145 Issue: 3 Pages: 1131-1140

    • DOI

      10.1090/proc/13387

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] C*-algebras associated with Hilbert C*-quad modules of C*-textile dynamical systems2016

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Journal of Mathematical Analysis and Application

      Volume: 438 Issue: 2 Pages: 578-628

    • DOI

      10.1016/j.jmaa.2016.02.020

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On flow equivalence of one-sided topological Markov shifts2016

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Proceedings of American Mathematical Society

      Volume: 144 Issue: 7 Pages: 2923-2937

    • DOI

      10.1090/proc/13074

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Continuous orbit equivalence of topological Markov shifts and dynamical zeta functions2016

    • Author(s)
      Kengo Matsumoto and Hiroki Matui
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 36 Issue: 5 Pages: 1557-1581

    • DOI

      10.1017/etds.2014.128

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] On the Markov Dyck shifts of vertex type2016

    • Author(s)
      kengo Matsumoto
    • Journal Title

      Discrete and Continuous dynemical Systems

      Volume: 36 Pages: 403-422

    • Related Report
      2015 Research-status Report
  • [Journal Article] Cuntz-Krieger algebras associated with Hilbert C*-quad modules of commuting matrices2015

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Mathematica Scandinavica

      Volume: 117 Pages: 126-149

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Strongly continuous orbit equivalence of one-sided topological markov shifts2015

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Journal of Operator Theory

      Volume: 74 Pages: 457-483

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] C*-algebras associated with textile dynamical systems2015

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      New York Journal of Mathematics

      Volume: 21 Pages: 1179-1245

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Subshifts , lambda-graph bysystems and their c*-algebras2019

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2019 Annual Research Report
  • [Presentation] Flow equivalence of topological Markov shifts and extended Ruelle algebras2018

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
  • [Presentation] Flip conjugacy of topological markov shifts and Ruelle algebras2018

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会
    • Related Report
      2018 Research-status Report
  • [Presentation] スメール空間からできるRuelle 環と両側Cuntz-Krieger 環2018

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会年会
    • Related Report
      2017 Research-status Report
  • [Presentation] strongly continuous orbit equivalence of topological Markov shifts and Cuntz-Kriger algebras2017

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2017-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] 双曲型力学系における漸近的連続軌道同型とRuelle環2017

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] Relative morita equivalence of Cuntz-Krieger algebras and flow equivalence of topological Markov shifts2017

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京
    • Related Report
      2016 Research-status Report
  • [Presentation] Strong Morita equivalence of C*-algebras v.s.strong shift equivalence of matrices2016

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      関西大学
    • Related Report
      2016 Research-status Report

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Published: 2015-04-16   Modified: 2021-02-19  

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