| Certain Cuntz Semigroup Properties of Certain Crossed Product C^*-algebras |
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| 作者姓名： | Qing Zhai FAN |
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| 作者单位： | Department of Mathematics |
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| 基金项目： | Supported by National Natural Sciences Foundation of China (Grant Nos. 11501357 and 11571008) |
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| 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.
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| 关 键 词： | C^*-algebras tracial APPROXIMATION Cuntz SEMIGROUP |
Certain Cuntz Semigroup Properties of Certain Crossed Product C*-algebras |
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| Qing Zhai FAN.Certain Cuntz Semigroup Properties of Certain Crossed Product C^*-algebras[J].Acta Mathematica Sinica,2020,36(3):337-362. |
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| Authors: | Fan Qing Zhai |
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| Institution: | Department of Mathematics, Shanghai Maritime University, Shanghai 201306, P. R. China |
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| Abstract: | 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. |
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| Keywords: | C*-algebras tracial approximation Cuntz semigroup |
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