Actions of amenable groups and crossed products of Z-absorbing C*-algebras

Abstract

We study actions of countable discrete amenable groups on unital separable simple nuclear Z-absorbing C*-algebras. Under a certain assumption on tracial states, which is automatically satisfied in the case of a unique tracial state, the crossed product is shown to absorb the Jiang-Su algebra Z tensorially.

arXiv comment15 pages

References in corpus (2)

• Nuclear dimension and Z-stability
• Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary

Cited by in corpus (7)

• Strongly self-absorbing C*-dynamical systems, III
• On a categorical framework for classifying C*-dynamics up to cocycle conjugacy
• Strongly outer actions of amenable groups on $\mathcal{Z}$-stable nuclear $C^{\ast }$-algebras
• Stable rank for crossed products by actions of finite groups on C*-algebras
• Rohlin actions of finite groups on the Razak-Jacelon algebra
• Actions of nonamenable groups on $\mathcal{Z}$-stable $C^{\ast }$-algebras
• Group actions on Smale space C*-algebras