Classification of Simple C*-Algebras: Inductive Limits of Matrix Algebras Over One-Dimensional Spaces

✍ Scribed by Liangqing Li

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 425 KB
• Volume: 192
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.2002.3895

✦ Synopsis

In this article, we will give a complete classification of simple C * -algebras which can be written as inductive limits of algebras of the form A n ¼ È kn i¼1 M ½n;i ðCðX n;i ÞÞ, where X n;i are arbitrary variable one-dimensional compact metrizable spaces. The results unify and generalize the previous results for the case X n;i ¼ S 1 and for the case of X n;i being trees. We obtain our classification results by reducing the case of general one-dimensional spaces to the case of circles. The techniques in this paper play important roles in the study of the case of higher-dimensional spaces. # 2002 Elsevier Science (USA)