降维区间代数的KK提升问题

重代数中投影的变形与非单C* 代数的冠代数的投影提升

Deformation of a projection in the multipleir algebra and projection lifting from the corona algebra of a non-simple C*-algebra

设$X$是单位区间或单位圆，$B$是$σ_p$ -有单位的纯无限单$C\sp*$ -代数，使得其乘子代数$M(B)$的秩为零.然后，我们确定了$C(X)\otimes B$的冠代数中的投影可提升到乘子代数中的投影的充要条件。这推广了L.布朗和作者\cite{BL}。主要技术工具分为两部分。第一部分借用了作者的前一篇论文（JFA 260（2011））。第二部分是证明在适当的“无限秩和余秩”条件下，我们可以在$C(X)\otimes B$的乘子代数中产生一个投影或余投影的子投影，其秩为K-理论数据的任意秩。

On the Decomposition Theorems for C*-algebras

Elliott dimension drop interval algebra is an important class among all $C^*$-algebras in the classification theory. Especially, they are building stones of $\mathcal{AHD}$ algebra and the latter contains all $AH$ algebras with the ideal property of no dimension growth. In this paper, we will show two decomposition theorems related to the Elliott dimension drop interval algebra. Our results are key steps in classifying all $AH$ algebras with the ideal property of no dimension growth.

Reduction to dimension two of local spectrum for $AH$ algebra with ideal property

A $C^{*}$-algebra $A$ has ideal property if any ideal $I$ of $A$ is generated as a closed two sided ideal by the projections inside the ideal. Suppose that the limit $C^{*}$-algebra $A$ of inductive limit of direct sums of matrix algebras over spaces with uniformly bounded dimension has ideal property. In this paper, we will prove that $A$ can be written as an inductive limit of certain very special subhomogeneous algebras, namely, direct sum of dimension drop interval algebras and matrix algebras over 2-dimensional spaces with torsion $H^{2}$ groups.