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Regularity Properties of Certain Crossed Product C*-Algebras

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Abstract

We show that the following properties of C* -algebras in a class Ω are inherited by simple unital C*-algebras in class TAΩ: (1) m-comparison of positive elements, (2) strong tracial m-comparison of positive elements, and (3) tracial nuclear dimension at most m. As an application, every unital simple C*-algebra with tracial topological rank at most k has tracial nuclear dimension at most k. Also as an application, let A be an infinite-dimensional simple unital exact 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 consider also.

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Acknowledgement

The research of first author was supported by grants from the National Natural Sciences Foundation of China (No. 11501357). The research of the second author was supported by a grant from the National Natural Sciences Foundation of China (No.11571008).

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  1. Department of Mathematics, Shanghai Maritime University, Shanghai, China, 201306

    Qingzhai Fan & Jun Yang

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  1. Qingzhai Fan
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  2. Jun Yang
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Correspondence to Qingzhai Fan or Jun Yang.

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Fan, Q., Yang, J. Regularity Properties of Certain Crossed Product C*-Algebras. Indian J Pure Appl Math 51, 1515–1531 (2020). https://doi.org/10.1007/s13226-020-0479-4

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  • DOI: https://doi.org/10.1007/s13226-020-0479-4

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