2014 Fiscal Year Final Research Report
Applications of operator algebras to symbolic dynamicaal systems
Project/Area Number |
23540237
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Global analysis
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Research Institution | Joetsu University of Education |
Principal Investigator |
MATSUMOTO Kengo 上越教育大学, 学校教育研究科(研究院), 教授 (40241864)
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Co-Investigator(Renkei-kenkyūsha) |
TOMIYAMA Jun 東京都立大学, 理学部, 名誉教授 (30006928)
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Project Period (FY) |
2011-04-28 – 2015-03-31
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Keywords | 作用素環 / 記号力学系 / C*環 / 位相的マルコフシフト / 軌道同型 |
Outline of Final Research Achievements |
I have studied symbolic dynamical systems and its C*-algebras from the following three view points. I have first studied typical examples of symbolic dynamical systems such as Dyck shifts and Markov-Dyck shifts and its C*-algebras. I have computed the K-groups of these C*-algebras. I have second introduced a notion of lambda-synchronization of subshifts with Wolfgang Krieger and proved that the lambda-synchronization is invariant under flow equivalence. Wolfgang Krieger and I have also presented formulae of zeta function and topological entropy for Markov-Dyck shifts. I have third studied continious orbit equivalence of one-sided topological markov shifts. Hiroki Matui and I have succeeded to obtain a complete classification theorem of continuous orbit equivalence of topological Markov shifts.
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Free Research Field |
作用素環論
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