On a topological invariance of non-commutative topological algebras

在本研究中，我们主要得到了两个关于O维代数的结果。其一是关于超有限II-1因子(或UHF C**-代数)的二元移位的外共轭。我们证明了任何二元移位都有无穷多个与原移位共轭但不是外共轭的移位。另一个问题是关于C**-动力系统。Cantor集的系统及其上的极小作用与该系统、Bratteli图及其上的一个序有关。在一些特殊的Bratteli图上定义了序，并研究了这些序的结构。因此，我们证明了有无数个Bratteli图是等价的，但不是顺序等价的。这些结果还在准备中。

In this research, we mainly get two results for O-dimensional algebras. One concerns with the outer conjugateness of binary shifts of hyperfinite II-1 factors(or UHF C**-algebras). We prove that any binary shift has infinitely many binary shifts which is conjugate, but not outer-conjugate to the original one. Another concerns a C**-dynamical system. The system of the Cantor set and a minimal action on it related to the system the Bratteli diagram and an order on it. We define orders on some special Bratteli diagram, and study these order structure. So we show that there is uncountable many Bratteli diagrams that are equivalent, but not order-equivalent.These results are in preparation.