实秩零ASH代数的分类与约化问题

C*-代数的分类问题一直是 C*-代数领域中一个十分核心的问题。自 Elliott 提出分类纲领以来，C*-代数的分类、不变量的特征和值域以及相应的约化问题，一直是该领域中一系列紧密关联的重要内容。单 C*-代数的相关工作，在学者们的不断努力下，已经取得了重大的突破。我们这里将要重点考虑的，是在实秩零这一非单性条件下的 ASH 代数的分类及相关问题。如果项目推进顺利，我们也将进一步考虑更为一般的具理想性质条件的情形。特别的，需要指出的是，我们针对的、具体研究的 SH 模块是一些具有良好结构的子齐次代数--- NCCW (非交换 CW 复形)。它们的构造本身便对应了拓扑在代数层面的非交换推广，是一类十分具体且重要的代数类。

The classification of C*-algebras has always been a crucial problem in the study of C*-algebras. Since Elliott proposed the classification program, the classification of C*-algebras, the characters and range of invariants and also the reduction problems under suitable condition have been a series of important parts in the study of this field. With great efforts of crowds of professors and scholars, the classification and relative problems of simple C*-algebras have made great breakthroughs already. The project we will focus on here, is the classification of ASH algebras and relative problems under the condition which are called real rank zero. Note that it is not the simplicity. If everything goes well, we will also try to push to the situation to a more general one, the ideal property. In particular, we should point out that the SH blocks we will concern here are those delicate sub-homogeneous algebras --- NCCW (non-commutative CW complex). The construction of such algebras corresponds to the generalization of topology at the non-commutative algebraic level, and indeed, they are quite concrete and important as a class of C*-algebras.