Applications of operator algebras to symbolic dynamicaal systems
Project/Area Number |
23540237
|
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
|
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)
|
Co-Investigator(Renkei-kenkyūsha) |
TOMIYAMA Jun 東京都立大学, 理学部, 名誉教授 (30006928)
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
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 / サブシフト / Cuntz-Krieger 環 / C*-環 / 軌道同型類 / HilbertC*-加群 |
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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Report
(5 results)
Research Products
(23 results)