Structure of operator algebras and its applications to Classification of symbolic dynamical systems

算子代数的结构及其在符号动力系统分类中的应用

• 批准号: 20540215
• 负责人: MATSUMOTO Kengo
• 金额: $ 2万
• 依托单位: Yokohama City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540215/
• 关键词: 作用素環; C*-環; 記号力学系; サブシフト; 軌道同型; 位相的マルコフシフト

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.

我主要研究了符号动力系统的轨道等价和相关的C^*-代数。研究结果发表在三篇论文中。特别地，证明了单侧拓扑Markov位移的连续轨道等价类与相应的保持Cartan子代数的Cuntz-Krieger代数的同构类完全对应.研究了由C^*-符号动力系统定义的C^*-代数的简单性条件和几个例子。研究了与具体非sofic子移位相关的C^*-代数的K-理论群。我开始研究温度的倒数不一定是真实的数的C^*-符号动力系统的KMS条件。

项目成果

Orbit equivalence in C*-algebras defined by actions of symbolic dynamical systems

由符号动力系统的作用定义的 C* 代数中的轨道等价

• 发表时间: 2009
• 期刊: Contemporary Mathematics 503巻
• 作者: Svensson Christa;富山淳;松本健吾
• 通讯作者: 松本健吾

タイルばりの作用からできるC*-環について

关于瓦梁作用形成的 C* 环

• 发表时间: 2010
• 作者: Wolfgang Krieger;松本健吾;松本健吾;松本健吾;Kengo Matsamoto;Kengo Matsumoto;Kengo Matsumoto;松本健吾
• 通讯作者: 松本健吾

Subshifts from one-counter codes

从单计数器代码换档

• 发表时间: 2009
• 作者: Wolfgang Krieger;松本健吾;松本健吾;松本健吾;Kengo Matsamoto;Kengo Matsumoto;Kengo Matsumoto;松本健吾;松本健吾;松本健吾;松本健吾-W. knger
• 通讯作者: 松本健吾-W. knger

Orbit equivalence of topological Markov shifts and Cuntz-Krieger algebras

拓扑马尔可夫位移和 Cuntz-Krieger 代数的轨道等价

• 发表时间: 2010
• 期刊: Pasific Journal of Mathematics 246巻
• 作者: 愛木豊彦;岡田真子;Yuki Nai to;Tetsuya Ishiwata;松本健吾
• 通讯作者: 松本健吾

Classification of ideals homeomorphism c*-algebras and quasidiagonality

理想同胚c*-代数和拟对角性的分类

• 发表时间: 2009
• 期刊: Acta applicable Mathematics 108巻
• 作者: Toyohiko AIRI;Jana Kopfova;Kengo Matsumoto;Yuki Naito;Toyohiko AIKI;Tetsuya Ishiwata;石井克幸;Kengo Matsumoto;Tetsuya Ishiwata;富山淳
• 通讯作者: 富山淳