Invariants of dynamical systems and its application to C* algebras and K-theory

在研究过程中，得到了维群嵌入的动态实现问题。关于动态实现的已知结果如下：假设给定两个维群之间的嵌入，则存在两个康托极小系统，其中一个几乎是另一个的一对一扩展，使得康托极小系统的关联维群与给定维群序同构。我们得到的结果是所谓的维群嵌入的符号动态实现问题。为了得到结果，我们使用了熵结构的概念。然而，我们在把这个概念应用到我们的问题上有一些困难。为此，我们对维群和熵结构技术进行了改进，最终得到了结果。

In the priod of my study, We got the result that dynamical realization problem of the embeddings of dimension groups. The known results with respect to dynamical realization is the following: Suppose an embedding between two dimension groups is given, then there exist two Cantor minimal systems, which one is an almost one-to-one extension of the other, such that associateddimension groups of Cantor minimial systems are order isomorphic to given dimension groups. The result we get is so-called the symbolic dynamical realization problem of the embeddings of dimension groups. In order to getthe result, we use the notion of the entoropy structure. However, we have some kind of difficulties to apply the notion to our problem. So we modify the tecniques of dimension groups and entropy structure and finally get the result.