On the classification of simple inductive limit $C^*$-algebras. I: The reduction theorem
On the classification of simple inductive limit $C^*$-algebras. I: The reduction theorem
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DOI：
10.4171/dm/127
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发表时间：
2002
影响因子：
0.9
通讯作者：
G. Gong
中科院分区：
文献类型：
--
作者：
G. Gong
假设这个公式是数学。是一个简单的C*-代数，其中Xn，i是一致有界维度的紧度量空间(这个限制可以放宽到维度增长非常慢的条件)。本文证明了A可以写成某些特殊三维空间上矩阵代数直和的一个归纳极限。因此，这类归纳极限C*-代数在随后与G.Elliott和L.Li(本系列的第二部分)的联合论文中被归类为Elliott不变量--由有序K-群和迹状态空间组成。(请注意，这类C*-代数不享受实秩零性质。)
Suppose that formula math. is a simple C*-algebra, where X n,i are compact metrizable spaces of uniformly bounded dimensions (this restriction can be relaxed to a condition of very slow dimension growth). It is proved in this article that A can be written as an inductive limit of direct sums of matrix algebras over certain special 3-dimensional spaces. As a consequence it is shown that this class of inductive limit C*-algebras is classified by the Elliott invariant - consisting of the ordered K-group and the tracial state space - in a subsequent paper joint with G. Elliott and L. Li (Part II of this series). (Note that the C*-algebras in this class do not enjoy the real rank zero property.).