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K-theory for C^* algebras aud its applications to symbolic dynamics

C^* 代数的 K 理论及其在符号动力学中的应用

基本信息

批准号：
14540213
负责人：
MATSUMOTO Kengo
金额：
$ 1.92万
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：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

In this research project, we have developed a theory of symbolic dynamics by using structure theory of C^*-algebras and its K-theory. We in particular have produced two joint research papers with professor Wolfgang Krieger (Germany, Heidelberg university). One is the paper A lambda-graph system for the Dyck shift and its K-groups (with W. Krieger), Documenta Math. 8(2003), 79-96 in which we have introduced a notion of Cantor horizon lambda-graph system for Dyck shifts and computed its K-theory group. The other one is the paper A lambda-graph system for the Dyck shift and its K-groups (with W. Krieger), Documenta Math. 8(2003), 79-96 in which we have introduced a notion of lambda-entropy for lambda-graph systems as a generalization of topological entropy. We also studied strong shift equivalence in symbolic dyanical systems in the two papers On strong shift equivalence of symbolic matrix systems, Ergodic Theory and Dynamical System 23(2003), 1551-1774 and Strong shift equivalence of symbolic dynamical systems and Morita equivalence of C^*-algebras, Ergodic Theory and Dynamical System 24(2004), 199-215. We also studied the C^*-algebra associated with a lambda-garph system of Motzkin shift in A simple purely infnite C^*-algebra associated with a lambda-graph system of the Motzkin shift, Math. Z. 248(2004), 369-39. Factor maps in symbolic dynamics have been studied in Factor maps of symbolic dynamics and inclusions of C^*-algebras, International J. Math. 15(2004), 313-339. Noncommutative topological entropy or D. Voiculescu on the C:-algebras associated with lambda-graph systems have been computed in the paper Topological entropy in C^*-algebras associated with lambda-graph systems, prerint, Ergodic Theory and Dynamical System (in press)

在本研究项目中，我们利用C^*-代数的结构理论及其K-理论发展了符号动力学理论。特别是，我们与沃尔夫冈·克里格教授(德国海德堡大学)共同撰写了两篇研究论文。一个是关于Dyck移位及其K-群的λ图系统(与W.Krieger合著)，Documenta Math。8(2003)，79-96，其中我们引入了Dyck位移的Cantor地平线λ图系统的概念，并计算了它的K-理论群。另一篇是关于Dyck移位及其K群的Lambda图系统(与W.Krieger合著)，Documenta Math。8(2003)，79-96，其中我们引入了Lambda-图系统的Lambda-熵的概念，作为拓扑熵的推广。我们也在两篇关于符号矩阵系统的强移位等价的文献[遍历理论与动力系统23(2003)，1551-1774和符号动力系统的强移位等价与C^*-代数的Morita等价，遍历理论与动力系统24(2004)，199-215]中研究了符号动力系统的强移位等价。我们还研究了与Motzkin移位的Lambda-garph系统相关的C^*-代数，以及与Motzkin移位的Lambda-Garph系统相关的一个简单的纯C^*-代数Math。Z.248(2004)，369-39.符号动力学中的因子映射和C^*-代数的包含中的因子映射已经被研究过，International J.Math。15(2004)，313-339。本文计算了与lambda-图系统有关的C~*-代数上的非对易拓扑熵或D.Voulescu。本文计算了与lambda-图系统、PRIMINT、遍历理论和动力系统有关的C^~*-代数的拓扑熵。