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K-theory for C^* algebras aud its applications to symbolic dynamics

Research Project

Project/Area Number 14540213
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

MATSUMOTO Kengo  Yokohama City University, Graduate School of integrated sciences, Assistant professor, 総合理学研究科, 助教授 (40241864)

Co-Investigator(Kenkyū-buntansha) ICHIRAKU Shigeo  Yokohama City University, Professor, 教授 (30046130)
ISHI Hideyuki  Yokohama City University, Asistant, 助手 (00326068)
Project Period (FY) 2002 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
KeywordsSymbolic dynamics / C^*-algebras / subshuts / K-theory / topological conjugacy invariant / C^*環 / ラムダグラフシステム / C^*-環
Research Abstract

In this research project, we have developed a theory of symbolic dynamics by using structure theory of C^*-algebras and its K-theory. We in particular have produced two joint research papers with professor Wolfgang Krieger (Germany, Heidelberg university). One is the paper A lambda-graph system for the Dyck shift and its K-groups (with W. Krieger), Documenta Math. 8(2003), 79-96 in which we have introduced a notion of Cantor horizon lambda-graph system for Dyck shifts and computed its K-theory group. The other one is the paper A lambda-graph system for the Dyck shift and its K-groups (with W. Krieger), Documenta Math. 8(2003), 79-96 in which we have introduced a notion of lambda-entropy for lambda-graph systems as a generalization of topological entropy. We also studied strong shift equivalence in symbolic dyanical systems in the two papers On strong shift equivalence of symbolic matrix systems, Ergodic Theory and Dynamical System 23(2003), 1551-1774 and Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C^*-algebras, Ergodic Theory and Dynamical System 24(2004), 199-215. We also studied the C^*-algebra associated with a lambda-garph system of Motzkin shift in A simple purely infnite C^*-algebra associated with a lambda-graph system of the Motzkin shift, Math. Z. 248(2004), 369-39. Factor maps in symbolic dynamics have been studied in Factor maps of symbolic dynamics and inclusions of C^*-algebras, International J. Math. 15(2004), 313-339. Noncommutative topological entropy or D. Voiculescu on the C:-algebras associated with lambda-graph systems have been computed in the paper Topological entropy in C^*-algebras associated with lambda-graph systems, prerint, Ergodic Theory and Dynamical System (in press)

Report

(4 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (38 results)

All 2005 2004 2003 Other

All Journal Article (31 results) Publications (7 results)

  • [Journal Article] K-theoretic invariants and conformal measures of the Dyck shifts2005

    • Author(s)
      K.Matsumoto
    • Journal Title

      International J.Math. 16

      Pages: 213-248

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The gradient maps associated to certain non-homogeneous cones2005

    • Author(s)
      H.Ishi
    • Journal Title

      Proc.Japan Acad.Ser.A Math.Sci 81

      Pages: 44-46

    • NAID

      40006898755

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] K-theoretic invariants and conformal measures of the Dyck shifts2005

    • Author(s)
      Matsumoto, K.
    • Journal Title

      International J. Math. 16

      Pages: 213-248

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] The gradient maps associated to certain non-homogeneous cones2005

    • Author(s)
      Ishi, H.
    • Journal Title

      Proc. Japan Acad. Ser. A Math. Sci. 81 no.3

      Pages: 44-46

    • NAID

      40006898755

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C*-algebras2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical System 24

      Pages: 199-215

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological conjugacy invariants of symbolic dynamics arising from C*-algebra K-theory2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Advanced Studies in Pure Math. 38

      Pages: 299-318

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A simple purely infnite C*-algebra associated with a lambda-graph system of the Motzkin shift2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Math.Zeitascrift 248

      Pages: 299-318

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A class of invariants of the topological conjugacy of subshifts2004

    • Author(s)
      W.Krieger, K.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical System 24

      Pages: 1155-1172

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Factor maps of symbolic dynamics and inclusions of OIL-algebras2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      International J.Math. 15

      Pages: 313-339

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Some remarks on the C*-algebras associated with subshifts2004

    • Author(s)
      T.M.Carlsen, K.Matsumoto
    • Journal Title

      Math.Scand. 95

      Pages: 145-160

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C^*-algebras2004

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Ergodic Theory and Dynamical System 24

      Pages: 199-215

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological conjugacy invariants of symbolic dynamics arising from C^*-algebra K-theory2004

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Advanced Studies in Pure Math. 38

      Pages: 299-318

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A simple purely infnite C^*-algebra associated with a lambda-graph system of the Motzkin shift2004

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Math. Z. 248

      Pages: 369-394

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A class of invariants of the topological conjugacy of subshifts2004

    • Author(s)
      Krieger, W., Matsumoto, K.
    • Journal Title

      Ergodic Theory and Dynamical System 24

      Pages: 1155-1172

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Factor maps of symbolic dynamics and inclusions of C^*-algebras2004

    • Author(s)
      Matsumoto, K.
    • Journal Title

      International J. Math. 15

      Pages: 313-339

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Some remarks on the C^*-algebras associated with subshifts, (with T. M. Carlsen)2004

    • Author(s)
      Carslsen, T.M., Matsumoto, K.
    • Journal Title

      Math. Scand. 95

      Pages: 145-160

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C^*-algebras.2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical System 24

      Pages: 199-215

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Topological conjugacy invariants of symbolic dynamics arising from C^*-algebra K-theory.2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Advanced Studies in Pure Mathematics 38

      Pages: 299-318

    • Related Report
      2004 Annual Research Report
  • [Journal Article] A simple purely infnite C^*-algebra associated with a lambda-graph system of the Motzkin shift2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      Mathematische Zeitshrift 248

      Pages: 369-394

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Factor maps of symbolic dynamics and inclusions of C^*-algebras2004

    • Author(s)
      K.Matsumoto
    • Journal Title

      International Journel of Mathematics 15

      Pages: 313-339

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Some remarks on the C^*-algebras associated with subshifts2004

    • Author(s)
      T.M.Carlsen, K.Matsumoto
    • Journal Title

      Mathematica Scandinavica 95

      Pages: 145-160

    • Related Report
      2004 Annual Research Report
  • [Journal Article] On strong shift equivalence of symbolic matrix systems2003

    • Author(s)
      K.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical System 23

      Pages: 1551-1774

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A lambda-graph system for the Dyck shift and its K-groups (with W.Krieger2003

    • Author(s)
      W.Krieger, K.Matsumoto
    • Journal Title

      Documenta Math. 8

      Pages: 79-96

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symbolic dynamics and C*-algebras2003

    • Author(s)
      K.Matsumoto
    • Journal Title

      Selected Papers on Analysis and Differential Equations, Amer.Math.Soc.Transl. 211

      Pages: 47-70

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] On strong shift equivalence of symbolic matrix systems2003

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Ergodic Theory and Dynamical System 23

      Pages: 1551-1774

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] A lambda-graph system for the Dyck shift and its K-groups2003

    • Author(s)
      Krieger, W., Matsumoto, K.
    • Journal Title

      Documenta Math. 8

      Pages: 79-96

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symbolic dynamics and C^*-algebras, in Selected Papers on Analysis and Differential Equations2003

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Amer. Math. Soc. Transl. (2) 211

      Pages: 47-70

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological entropy in C*-algebras associated with lambda-graph systems

    • Author(s)
      K.Matsumoto
    • Journal Title

      Ergodic Theory and Dynamical System (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Construction and pure infniteness of C*-algebra associated with lambda-graph systems

    • Author(s)
      K.Matsumoto
    • Journal Title

      Math Scand. (印刷中)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Topological entropy in C^*-algebras associated with lambda-graph systems

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Ergodic Theory and Dynamical System, (prerint) (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Construction and pure infiniteness of C^*-algebras associated with lambda-graph systems

    • Author(s)
      Matsumoto, K.
    • Journal Title

      Math. Scand. (in press)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Publications] K.Matsumoto: "On strong shift equivalence of symbolic matrix systems"Ergodic Theory and Dynamical Systems. 23巻. 1551-1574 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] W.Krieger, K.Matsumoto: "A lambda-graph systems for the Dyck shifts and its K-groups"Documenta Mathematics. 8巻. 79-96 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Matsumoto: "Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C^*-algebras"Ergodic Theory and Dynamical Systems. 24巻. 199-215 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Matsumoto: "A simple purely infinite C^*-algebras associated with a lambda-graph system of the Motzkin shift"Mathematiche Zeitscrift. (発表予定).

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Matsumoto: "C^*-algebras associated with presentations of subshifts"Documenta Mathematica. 7巻. 1-30 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Matsumoto: "Shannon graphs, subshifts and lambda-graph systems"Journal of Mathematical Society of Japan. 54巻. 877-899 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] K.Matsumoto: "On strong shift equivalence of symbolic matrix systems"Ergodic Theory and Dynamical Systems. (発表予定).

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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