Quasidiagonal traces and crossed products
Abstract
Let $A$ be a simple, exact, separable, unital $C^*$algebra and let $\alpha \colon G \rightarrow Aut(A)$ be an action of a finite group $G$ with the weak tracial Rokhlin property. We show that every trace on $A \rtimes_{\alpha} G$ is quasidiagonal provided that all traces on $A$ are quasidiagonal. As an application, we study the behavior of finite decomposition rank under taking crossed products by finite group actions with the weak tracial Rokhlin property. Moreover, we discuss the stability of the property that all traces are quasidiagonal under taking crossed products of finite group actions with finite Rokhlin dimension with commuting towers.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.06990
 arXiv:
 arXiv:1609.06990
 Bibcode:
 2016arXiv160906990F
 Keywords:

 Mathematics  Operator Algebras
 EPrint:
 To appear in Indiana U. Math. J