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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Supported by National Natural Sciences Foundation of China (Grant Nos. 11501357 and 11571008)
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Fan, Q.Z. Certain Cuntz Semigroup Properties of Certain Crossed Product C*-algebras. Acta. Math. Sin.-English Ser. 36, 337–362 (2020). https://doi.org/10.1007/s10114-020-9375-4
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DOI: https://doi.org/10.1007/s10114-020-9375-4