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Regularity Properties of Certain Crossed Product C*-Algebras

Author

Listed:
  • Qingzhai Fan

    (Shanghai Maritime University)

  • Jun Yang

    (Shanghai Maritime University)

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.

Suggested Citation

  • Qingzhai Fan & Jun Yang, 2020. "Regularity Properties of Certain Crossed Product C*-Algebras," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1515-1531, December.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:4:d:10.1007_s13226-020-0479-4
    DOI: 10.1007/s13226-020-0479-4
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