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

主要研究了符号动力系统及其相关的C^*-代数的轨道等价。研究结果已发表在三篇论文中。特别地，证明了单侧拓扑马尔可夫移位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。还研究了由C^*-符号动力系统定义的C^*-代数的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。我已经开始研究逆温度不一定是实数的C^*-符号动力系统的KMS条件。

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.