• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

C*-環とその記号力学系、双曲型力学系の分類、軌道同型の研究への応用

Research Project

Project/Area Number 19K03537
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12010:Basic analysis-related
Research InstitutionJoetsu University of Education

Principal Investigator

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

Project Period (FY) 2019-04-01 – 2025-03-31
Project Status Granted (Fiscal Year 2023)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
KeywordsC*-環 / 記号力学系 / Cuntz-Krieger 環 / K-群 / 拡大群 / 位相的マルコフシフト / 連続軌道同型 / 双曲型力学系 / サブシフト / C*-環 / 作用素環 / Cuntz-Krieger algebra / 軌道同型 / スメール空間
Outline of Research at the Start

今まで位相的マルコフシフトに対してなされてきた
(1) 力学系の軌道同型類、(2) 力学系の充足群の分類、(3) 力学系のゼータ関数、
(4) エタール亜群の同型類、(5) C*-環のKー理論、(6) C*-環とそのカルタン部分環の分類、(7) C*-環のゲージ作用の分類
の対応を、スメール空間というコンパクト距離空間上の同相写像からなる双曲型位相力学系
に対して行うという壮大な試みが本研究の概要である。またさらに位相的マルコフシフトとは限らない一般の記号力学系に対しても上記の対応関係を明らかにしたい。

Outline of Annual Research Achievements

2023年度は9月と1月に京都大学数理解析研究所で行われた作用素環論研究集会、10月のエルゴード理論研究集会、2月に金沢大学で行われた数論とエルゴード理論研究集会、3月に大阪公立大学で行われたの日本数学会年会等に参加し、作用素環論、エルゴード理論の研究者と積極的に交流した。特に、1月に京都大学で行われた研究集会で曽我部太郎氏(京都大学)のKK-理論的なC*-環の拡大における双対性の講演に触発され、曽我部氏と京都大学や大阪公立大学で討論を重ね、preprint「On the homotopy groups of the automorphism groups of Cuntz-Krieger algebras」を共同研究としてarxivに投稿できた。この共著論文では位相的マルコフシフトに付随してできるCuntz-Krieger環の自己同型群のホモトピー群がCuntz-Krieger 環の完全不変量であることが証明でき、位相的マルコフシフトの新たな不変量を導入することができた。同時に環の強拡大群と弱拡大群の二つが環の完全不変量であることも証明された。また 記号力学系に付随してできるC*-環の強拡大群と弱拡大群の計算公式を発見し、preprint「Extension groups for the C*-algebras associated with lambda-graph systems」を現在執筆中である。さらに位相的マルコフシフトのeventual conjugacyについて、その力学系的特徴づけ、等をまとめてpreprint「Structure of eventual conjugacy of one-sided topological Markov shits and isomorphisms of Cuntz-Krieger algebras」を完成させた。

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

双曲型力学系の中の記号力学系特に位相的マルコフシフトからできるC*環について、その自己同型群のホモトピー群が環の完全不変量であることを曽我部太郎氏(京都大学理)との共同研究で発見できた。さらに、位相的マルコフシフトのeventual conjugacyについて、その力学系的特徴づけ等をまとめてpreprint「Structure of eventual conjugacy of one-sided topological Markov shits and isomorphisms of Cuntz-Krieger algebras」を完成させるこことができた。別のpreprint 、「Extension groups for the C*-algebras associated with lambda-graph systems」を現在執筆中である。また曽我部氏とのC*-環の自己同型群のホモトピー群の研究も位相的マルコフシフトからできるC*-環に関連して、現在継続できている。

Strategy for Future Research Activity

記号力学系からできるC*-環の不変量としての強拡大群、弱拡大群の様々な例の計算をおこうよていである。またこの計算は記号力学系のみならず、双曲型力学系からできるC*ー環にも適用できそうなので、その軌道構造を見ながら発展させたい。また曽我部太郎氏と位相的マルコフシフトからできるC*環について、その自己同型群のホモトピー群が環の完全不変量であることをつきとめたので、この結果もCuntz-Krieger 環のみならずもっと広いクラスのKirchberg 環や、双曲型力学系からできるC*ー環に拡張することを試みたいと考えている。

Report

(5 results)
  • 2023 Research-status Report
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (27 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (1 results) Journal Article (24 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 23 results,  Open Access: 22 results) Presentation (2 results) (of which Invited: 1 results)

  • [Int'l Joint Research] Heidelberg University/Institute of Applied Mathematics(ドイツ)

    • Related Report
      2019 Research-status Report
  • [Journal Article] Subgroups of continuous full groups and relative continuous orbit equivalences of one-sided topological Markov shifts2023

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 525 Issue: 1 Pages: 127230-127230

    • DOI

      10.1016/j.jmaa.2023.127230

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Corrigendum to “Uniformly continuous orbit equivalence of Markov shifts and gauge actions on Cuntz?Krieger algebras”2023

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 151 Pages: 5469-5471

    • DOI

      10.1090/proc/16314

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] One-sided topological conjugacy of topological Markov shifts, continuous full groups and Cuntz?Krieger algebras2023

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Dynamical Systems

      Volume: 38 Issue: 4 Pages: 541-555

    • DOI

      10.1080/14689367.2023.2218601

    • Related Report
      2023 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finitely presented isomorphisms of Cuntz-Krieger algebras and continuous orbit equivalence of one-sided topological Markov shifts2023

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      MATHEMATICA SCANDINAVICA

      Volume: 129 Issue: 3 Pages: 613-630

    • DOI

      10.7146/math.scand.a-139804

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Simple purely infinite $C^*$-algebras associated with normal subshifts2023

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Documenta Mathematica

      Volume: 28 Issue: 3 Pages: 603-669

    • DOI

      10.4171/dm/915

    • Related Report
      2023 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts2022

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Discrete & Continuous Dynamical Systems

      Volume: 42 Issue: 2 Pages: 841-841

    • DOI

      10.3934/dcds.2021139

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] C*-ALGEBRAS ASSOCIATED WITH TWO-SIDED SUBSHIFTS2022

    • Author(s)
      MATSUMOTO KENGO
    • Journal Title

      Journal of the Australian Mathematical Society

      Volume: 112 Issue: 2 Pages: 230-263

    • DOI

      10.1017/s144678872000049x

    • Related Report
      2022 Research-status Report 2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On simplicity of the C*-algebras associated with λ-graph systems2022

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 515 Issue: 2 Pages: 126441-126441

    • DOI

      10.1016/j.jmaa.2022.126441

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On one-sided topological conjugacy of topological Markov shifts and gauge actions on Cuntz-Krieger algebras2022

    • Author(s)
      MATSUMOTO KENGO
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 42 Issue: 8 Pages: 2575-2582

    • DOI

      10.1017/etds.2021.53

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On certain inverse semigroups associated with one-sided topological Markov shifts2022

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Semigroup Forum

      Volume: 105 Issue: 2 Pages: 508-516

    • DOI

      10.1007/s00233-022-10309-y

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On a family of C*-subalgebras of Cuntz-Krieger algebras2022

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Acta Scientiarum Mathematicarum

      Volume: 88 Issue: 3-4 Pages: 739-767

    • DOI

      10.1007/s44146-022-00047-6

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] One-sided topological conjugacy of normal subshifts and gauge actions on the associated C*-algebras2021

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Dynamical Systems

      Volume: 36 Issue: 4 Pages: 586-607

    • DOI

      10.1080/14689367.2021.1970115

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] An etale equivalence relation on a tiling space arising from a two-sided subshift and associated C*-algebras2021

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Dynamical Systems

      Volume: 36 Issue: 3 Pages: 445-482

    • DOI

      10.1080/14689367.2021.1928605

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] On one-sided topologicaal conjugacy of topological Markov shifts and gauge actions on Cuntz-Krieger lgebras2021

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Ergodic Theory and Dynamical Systems

      Volume: 0

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] C*-algebras associated with asymptotic equivalence relations defined by hyperbolic toral automorphisms2021

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Electronic Research Archive

      Volume: 0 Issue: 4 Pages: 2645-2656

    • DOI

      10.3934/era.2021006

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Coded equivalence of one-sided topological Markov shifts2021

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Theoretical Computer Science

      Volume: 855 Pages: 133-140

    • DOI

      10.1016/j.tcs.2020.11.044

    • Related Report
      2020 Research-status 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
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Continuous orbit equivalence of topological Markov shifts and KMS states on Cuntz-Krieger algebras2020

    • Author(s)
      Matsumoto Kengo
    • Journal Title

      Discrete & Continuous Dynamical Systems - A

      Volume: 40 Issue: 10 Pages: 5897-5909

    • DOI

      10.3934/dcds.2020251

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [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
      2020 Research-status Report 2019 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Continuous orbit equivalence of topological Markov shifts and KMS states of Cuntz-Krieger algebras2020

    • Author(s)
      Kengo Matsumoto
    • Journal Title

      Discrete and Continuous Dynamical Systems

      Volume: -

    • Related Report
      2019 Research-status Report
    • 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 Research-status 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 Research-status 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 Issue: 5 Pages: 1243-1296

    • DOI

      10.4153/cjm-2018-012-x

    • Related Report
      2019 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 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 記号力学系における軌道同型、位相共役とC*-環について2021

    • Author(s)
      松本 健吾
    • Organizer
      日本数学会年会(慶応大学)
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Subshifts and lambda-graph bisystems 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 Research-status Report

URL: 

Published: 2019-04-18   Modified: 2024-12-25  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi