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

在本研究计划中，我们利用C^*-代数的结构理论和它的K-理论建立了一个符号动力学理论。我们特别与Wolfgang Krieger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位移及其K-群的一个图解系统（与W. Krieger），Documenta Math.8（2003），79-96，其中我们引入了用于Dyck移位的Cantor视界图系统的概念，并计算了其K-理论群。另一篇是关于Dyck位移及其K-群的一个图解系统（与W。Krieger），Documenta Math.8（2003），79-96，其中我们已经引入了用于图系统的图熵的概念作为拓扑熵的推广。我们还研究了符号动力系统中的强移位等价，在两篇论文On strong shift equivalence of symbolic matrix systems，Ergodic Theory and Dynamical System 23（2003），1551-1774和Strong shift equivalence of symbolic dynamic systems and Morita equivalence of C^*-algebras，Ergodic Theory and Dynamical System 24（2004），199-215中。我们还研究了与Motzkin位移的一个简单纯无限C^*-代数，数学Z. 248（2004），369-39.符号动力学中的因子映射已经在Factor maps of symbolic dynamics and inclusion of C^*-algebras，International J. Math.15（2004），313-339中进行了研究。非交换拓扑熵或D。Voiculescu在《拓扑熵在C^*-代数中的应用》一文中计算了C^*-代数的拓扑熵，并给出了遍历理论和动力学系统（待出版）。

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)