Asymptotic Direct System of C^(*)-algebras and Locally AF-algebra  

C^(*)-代数渐近顺向系统和局部AF-代数

作　　者：XIE Zhentao YAO Hongliang WANG Hao 谢镇涛;姚洪亮;王浩(南京理工大学数学与统计学院,江苏南京210094)

机构地区：[1]School of Mathematics and Statistics,Nanjing University of Science and Technology,Nanjing,Jiangsu,210094,P.R.China

出　　处：《数学进展》2024年第5期1084-1092,共9页Advances in Mathematics（China）

基　　金：Supported by Natural Science Foundation of Jiangsu Province,China (No.BK20171421)。

摘　　要：We define the direct limit of the asymptotic direct system of C^(*)-algebras and give some properties of it.Finally,we prove that a C^(*)-algebra is a locally AF-algebra,if and only if it is the direct limit of an asymptotic direct system of finite-dimensional C^(*)-algebras.本文首先定义了C^(*)-代数渐近顺向系统的归纳极限并给出了它的一些性质,最后证明了C^(*)-代数是局部AF-代数等价于它是某个有限维C^(*)-代数渐近顺向系统的归纳极限.

关 键 词：C^(*)-algebra asymptotic direct system direct limit locally AF-algebra 

分 类 号：O177.2[理学—数学]