Regularity Properties of Certain Crossed Product C*-Algebras

Qingzhai Fan () and Jun Yang ()
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Qingzhai Fan: Shanghai Maritime University
Jun Yang: Shanghai Maritime University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1515-1531

Abstract: 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.

Keywords: C*-algebras; tracial approximation; Cuntz semgroup; 46L35; 46L05; 46L80 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0479-4

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