Certain Cuntz Semigroup Properties of Certain Crossed Product C^*-algebras  

作　　者：Qing Zhai FAN 

机构地区：[1]Department of Mathematics,Shanghai Maritime University,Shanghai 201306,P.R.C hina

出　　处：《Acta Mathematica Sinica,English Series》2020年第3期337-362,共26页数学学报（英文版）

基　　金：Supported by National Natural Sciences Foundation of China(Grant Nos.11501357 and 11571008)。

摘　　要：We show that the following properties of the C^*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C^*-algebra C^*(G,A,α) also has the property under consideration.We show that the following properties of the C*-algebras in a class Ω are inherited by simple unital C-algebras in the class TAΩ:(1)(m,n)-decomposable,(2) weakly(m,n)-divisible,(3) weak Riesz interpolation.As an application,let A be an infinite dimensional simple unital C-algebra such that A has one of the above-listed properties.Suppose that α:G→Aut(A) is an action of a finite group G on A which has the tracial Rokhlin property.Then the crossed product C*-algebra C*(G,A,α) also has the property under consideration.

关 键 词：C^*-algebras tracial APPROXIMATION Cuntz SEMIGROUP 

分 类 号：O153[理学—数学]