On a topological invariance of non-commutative topological algebras

在本研究中，我们主要得到了O-维代数的两个结果。一个是超有限II-1因子（或UHF C**-代数）的二元移位的外共轭性。证明了任意二进制移位都有无穷多个二进制移位共轭，但不是外共轭的。另一个是关于C**-动力系统。Cantor集系统及其上的极小作用与系统的Bratteli图及其上的序有关，我们定义了某些特殊的Bratteli图上的序，并研究了这些序的结构。因此，我们证明了有无数的Bratteli图是等价的，但不是序等价的。

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.