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2001 Fiscal Year Final Research Report Summary

K-Theory for C*- algebras and its applications to Symbolic dynamics

Research Project

Project/Area Number 12640204
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  Graduate School of Integrated Science, Yokohama City University, Associated Professor, 理学部, 助教授 (40241864)

Co-Investigator(Kenkyū-buntansha) FUJII Kazuyuki  Graduate School of Integrated Science, Yokohama City University, Professor, 理学部, 教授 (00128084)
ICHIDA Ryosuke  Graduate School of Integrated Science, Yokohama City University, Professor, 理学部, 教授 (10094294)
ICHIRAKU Shigeo  Graduate School of Integrated Science, Yokohama City University, Professor, 理学部, 教授 (30046130)
ISHI Hideyuki  Graduate School of Integrated Science, Yokohama City University, Research Assistant, 理学部, 助手 (00326068)
Project Period (FY) 2000 – 2001
KeywordsC^*-algebras / symbolic dynamics / subshifts / K-Theory / Ext-groups
Research Abstract

Symbolic dynamics is a class of topological dynamical systems. It contains a clss of topological Markov shifts and sofic systems. In this research project, symbolic dynamics has been studied by using functional analytic method of C*-algebras. As a concrete result of this research, the Bowen-Franks groups for subshifts defined by the Ext-groups for the associated C*-algebras have been proved to be invariant under flow equivalence by using C*-algebra method (K-Theory 23(2001), 67-104). The result has been also proved by using a generalizing method of Bowen-Franks's argument for topological Markov shifts without using C*-algebra method. The Bowen-Franks groups for certain subshifts such as Dyck shifts have been computed so that it has been shown that some subshifts with the same topological entropy are not flow equivalent each other. We find presentations of subshifts in the structure of the Bratteli diagram of the AF-algebras inside the C*-algebras associated with subshifts and call them λ-graph systems. A relationship among λ-graph systems, subshifts and Schannon graphs has been studied in a joint work with Professor Wolfgang Krieger (Heidelberg University, Germany). In the joint work, a new class of subshifts called protosynchronizations has been introduced (to appear in J. Math. Soc. Japan). A construction of C*-algebras associated with λ-graph systems has been introduced in a preprint entitled "C*-algebras associated with presentations of subshifts. "These results hav been also published in the Japanese journal "Suugaku" and will be published in its english translation "Suugau Exposition."

  • Research Products

    (18 results)

All Other

All Publications (18 results)

  • [Publications] K.Matsumoto: "On ciutomorphisms of C^*-algebras associated with subshifts"Journal of Operator Theory. 44. 91-112 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Matsumoto: "Stabilized C^*-algebras constructed from symbolic dynamical systems"Ergodic Theory and Dynamical Systems. 20. 921-841 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Matsumoto: "Bowen-Franks groups as invariant of flow equivalent of subshifts"Ergodic Theory and Dynamical Systems. 21. 1831-1842 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Matsumoto: "Bowen-Franks groups for subshifts and Ext-groups for C^*-algebras"K-Theory. 23. 67-104 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 松本健吾: "記号力学系とC^*-環"数学. 53. 259-278 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] W.Krieger: "Shannon graphs, subshifts and lambda-graph systems"Journal of Mathematical Society of Japan. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Matsumoto: "Symbolic dynamics and C^*-algebras"Sugaku Exposition. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Fujii: "Note on coherent states and adiabatic connection curvatures"Journal of Mathematical Physics. 41. 4406-4412 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Ishii: "Basic relative invariants associated to homogeneous cones and applications"Journal of Lie Theory. 11. 155-171 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K. Matsumoto: "On automorphisms of C*-algebras associated with subshifts"J. Operator Theory. 44. 91-112 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Matsumoto: "Stabilized C*-algebras constructed from symbolic dynamical systems"Ergodic Theory Dynam. Systems. 20. 821-841 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Matsumoto: "Bowen-Franks groups as an invariant for flow equivalence of subshifts"Ergodic Theory Dynam. Systems. 21. 1831-1842 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Matsumoto: "Bowen-Franks groups for subshifts and Ext-groups for C*-algebras"K-Theory. 23. 67-104 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Matsumoto: "Symbolic dynamics and C*-algebras (in Japanese)"Suugaku. 53. 259-278 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] W. Krieger and K. Matsumoto: "Shannon graphs, subshifts and lambdagraph systems"J. Math. Soc. Japan. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Matsumoto: "Symbolic dynamics and C*-algebras"Sugaku Exposition. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K. Fujii: "Note on coherent states and adiabatic connections curvatures"J. Math. Phy.. 41. 4406-4412 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Ishi: "Basic relative invariants associated to homogeneous cones and applications"J. Lie Theory. 11. 155-171 (2001)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2003-09-17  

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