2001 Fiscal Year Final Research Report Summary
K-Theory for C*- algebras and its applications to Symbolic dynamics
| Project/Area Number |
12640204
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Yokohama City University |
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Principal Investigator |
MATSUMOTO Kengo Graduate School of Integrated Science, Yokohama City University, Associated Professor, 理学部, 助教授 (40241864)
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| 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)
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| Project Period (FY) |
2000 – 2001
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| Keywords | C^*-algebras / symbolic dynamics / subshifts / K-Theory / Ext-groups |
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| 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."
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