Simple generalized inductive limits of C^(*)-algebras

作     者：Xuanlong Fu Xuanlong Fu

作者机构：Department of Mathematics and the Research Center for Operator AlgebrasEast China Normal UniversityShanghai 200062China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2021年第64卷第5期

页      面：1029-1044页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the Research Center for Operator Algebras at East China Normal University which is funded by the Science and Technology Commission of Shanghai Municipality (Grant No.13dz2260400) National Natural Science Foundation of China (Grant No.11531003) Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice (Grant No.1361431) the special fund for the Short-Term Training of Graduate Students from East China Normal University 

主　　题：C^(*)-algebras generalized inductive limit simplicity approximately divisible tracial rank zero 

摘      要：We give a necessary and sufficient condition where a generalized inductive limit becomes a simple C^(*)-algebra. We also show that if a unital C^(*)-algebra can be approximately embedded into some tensorially self absorbing C^(*)-algebra C(e.g., uniformly hyperfinite(UHF)-algebras of infinite type, the Cuntz algebra O_(2)),then we can construct a simple separable unital generalized inductive limit. When C is simple and infinite(*** infinite), the construction is also infinite(resp. properly infinite). When C is simple and approximately divisible, the construction is also approximately divisible. When C is a UHF-algebra and the connecting maps satisfy a trace condition, the construction has tracial rank zero.