Classification of automorphisms of C^*-algebras

利用KK理论得到了实秩0的简单AT代数自同构的外类的分类结果。在这样做的过程中，我们引入了有序扩展的新概念，将有序结构结合到通常的扩展中，这是一个在纯无限C^*-代数中不会出现的新特征。并对某些AF代数的迹标自同态进行了分类。这是先前由首席研究员等人得到的类似结果的推广。对于一些特定的自同构，证明了Rohlin性质，这些自同构远非近似内但保持痕迹。因此，这是一个不包括在上述结果中的例子。给出了UHF代数和AF代数的单参数自同构群的一些新的例子。这就解决了一段时间以来一直难以解决的一些老问题，为这一老领域开辟了新的前景。在自同构（或渐近内自同构）作用下，证明了可分离简单C^*-代数的纯状态空间的齐性。这也解决了一个老问题，揭示了C^*-代数的内部结构。

A classification result was obtained for outer classes of automorphisms of simple AT algebras of real rank zero in terms of KK theory. In doing so we introduced a new notion of ordered extension incorporating an order structure to the usual extensions, which is a new feature that does not show up in the case of purely infinite C^*-algebras.Also a classification result was obtained for trace-scaling autmorphisms of certain AF algebras. This is an extension of similar results previously obtained by the head investigator et al.The Rohlin property was shown for some specific automorphisms, which are far from approximately inner but trace-preserving. Thus this is an example which is not covered by the above-mentioned results.Some novel examples were given to one-parameter automorphism groups of UHF algebras and AF algebras. This solves some old problems which have been resisting a solution for some time and opens up a new prospect to this old field.The homogeneity was shown for the pure state space of a separable simple C^*-algebra under the action of automorphisms (or asymptotically inner automorphisms). This also solves an old problem and reveals an inner structure of such a C^*-algebra.