2004 Fiscal Year Final Research Report Summary
K-theory for C^* algebras aud its applications to symbolic dynamics
| Project/Area Number |
14540213
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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 Yokohama City University, Graduate School of integrated sciences, Assistant professor, 総合理学研究科, 助教授 (40241864)
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| Co-Investigator(Kenkyū-buntansha) |
ICHIRAKU Shigeo Yokohama City University, Professor, 教授 (30046130)
ISHI Hideyuki Yokohama City University, Asistant, 助手 (00326068)
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| Project Period (FY) |
2002 – 2004
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| Keywords | Symbolic dynamics / C^*-algebras / subshuts / K-theory / topological conjugacy invariant |
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| 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)
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