AH代数上的有限群作用

算子代数上群作用的研究是算子代数中的一个核心问题.在本项目中,我们将以Blackadar提升问题为着眼点,利用单核C*-代数分类理论,研究AH代数的有限群作用及其产生的交叉积C*-代数的性质.具体研究内容包括:1.在群作用提升方面,我们将考虑Blackadar提升问题,有限群版本的Lin-Osaka问题和广义Blackadar提升问题;2.在AH代数有限群作用产生的交叉积C*-代数方面,我们拟研究将AH代数在有限群作用在K-理论层面上保持不变的情况下,产生的交叉积C*-代数的广泛性和多样性.此外,我们还将研究单的AH代数上有限群归纳极限型作用的分类.

Group actions are essential for understanding the structure of operator algebras. In this project, based on Blackadar lifting problem, we will extensively study the finite group actions on AH algebras and the properties of the related crossed product C*-algebras by using the classification theory of nuclear C*-algebras. The main topics are: 1.In the aspect of lifting of group actions,we will consider Blackadar lifting problem, finite group version of Lin-Osaka problem, and generalized Blackadar lifting problem as well. 2.In the aspect of the crossed product C*-algebras generated by finite groups acting on AH algebras, we shall study the generality and diversity of the crossed product C*-algebras. In addition, we will also explore the classification of product type actions of finite groups actions on simple AH algebras.