2007 Fiscal Year Final Research Report Summary
Structure theory of C*-algebras and its application of classification of symbolic dynamics
| Project/Area Number |
17540200
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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, College of Arts and Sciences, Assistant professor (40241864)
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| Co-Investigator(Kenkyū-buntansha) |
FUJII Kazuyuki Yokohama City University, International Collage of Arts and Sciences, Professor (00128084)
TOMIYAMA Jun Tokyou Metropolotan University, Faculty of Science, Emeritus Professor (30006928)
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| Project Period (FY) |
2005 – 2007
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| Keywords | C^*-algebras / symbolic dynamical systems |
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| Research Abstract |
In order to construct classification theory of symbolic dynamics from the view point of C^*-algebras, we have studied algebraic structure and several important examples of lambda-graph systems which preset symbolic dynamical systems. As concrete examples we have studied the Cantor horizon lambda-graph systems presenting Dyck shifts ,shown their simplicity and computed their K groups. We also show that there is a bijective correspondence between hereditary invariant subsystems and ideals of the associated C^*-algebras. We have clarified structure of periodic points of lambda-graph systems. We have formulated action of symbolic dynamics on C^*-algebras and constructed crossed products of the actions. The C^*-algebras are invariant under strong shift equivalence of actions. Hence their stably isomorphic classes are invariant under strong shift equivalence of the actions so that its K groups are invariant. We also generalize strong shift equivalence to Hilbert C^*-bimodules. As joint work with W. Krieger, we have studied one-counter codes.
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