Simple generalized inductive limits of C*-algebras

• 作者: Xuanlong Fu
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（5）
• 所属期刊栏目: Articles
• 页码范围: 1029-1044
• 页数: 16页
• 语种: 英文

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 O2),then we can construct a simple separable unital generalized inductive limit.When C is simple and infinite (resp.properly 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.