交叉积C*-代数若干问题的研究

The study of C*-algebra dynamical systems and the associated crossed product C*-algebras is one of important branches of operator algebra, which is related to such diverse fields as operator theory, group representations, topology, quantum mechanics, non-commutative geometry and topological dynamical systems. This study is concentrated to some basic properties of C*-algebra crossed products, which provide a powerful tool to the classification of crossed product C*-algebras.. The Rokhlin property of locally compact topological group actions on original algebras has general sense. In this program we study crossed product algebra properties by finte group or integer group actions with Rokhlin property. We study the hereditary property of tracial ranks between original albebras and the associatied crossed algebras, the automorphism conjugacy relation of origina algebras and the homorphism relation of the associated crossed products, AF-embedding of crossed products, etc.

C*-代数动力系统以及相应的交叉积C*-代数的研究是算子代数的重要研究分支之一，它的研究对于相关学科如：算子理论、群表示论、拓扑学、量子力学、非交换几何、拓扑动力系统等都有很大的推动作用。本课题将集中研究C*-代数交叉积的若干基本性质，为交叉积C*-代数的分类研究提供有力工具。. 原代数上局部紧拓扑群作用的Rokhlin性质具有普遍意义，本课题研究具有迹Rokhlin性质的有限群或整数群作用所生成的交叉积的代数性质，特别是在原代数为无限维的单的或非单的有单位元的C*-代数的情况下，我们考察原代数与相应交叉积的的迹秩的遗传性、原代数原代数上自同构共轭关系与相应交叉积的同态关系、交叉积的AF-嵌入等问题。

我们研究了对于原代数为一般的C*-代数的动力系统，得到了其上两个*-自同构弱逼近共轭的一个充分条件, 以及三重K群交换套图，.同时研究了弱逼近共轭和逼近套-共轭之间的关系。我们得到了在具有迹Rokhlin性质的有限群作用下，原代数与交叉积C*-代数之间迹类性质的遗传性。