2010 Fiscal Year Final Research Report
Structure of operator algebras and its applications to Classification of symbolic dynamical systems
| Project/Area Number |
20540215
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Yokohama City University |
|---|
Principal Investigator |
MATSUMOTO Kengo Yokohama City University, 大学院・学校教育研究科, 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) |
2008 – 2010
|
| Keywords | 作用素環 / C*-環 / 記号力学系 / サブシフト / 軌道同型 |
|---|
| Research Abstract |
I have studied mainly orbit equivalence of symbolic dynamical systems and related C^*-algebras. The results have been published in three papers. Especially, it has been proved that the continuous orbit equivalence classes of one-sided topological Markov shifts exactly correspond to the isomorphism classes of the associated Cuntz-Krieger algebras keeping their Cartan subalgebras. I also studied simplicity condition and several examples of C^*-algebras defined by C^*-symbolic dynamical systems. K-theory groups for C^*-algebras associated with concrete non sofic subshifts have been studied. I have began to study KMS condition for C^*-symbolic dynamical systems for which inverse temperatures are not necessarily real numbers.
|
