Regularity properties and Rokhlin dimension for compact group actions

Abstract

We show that formation of crossed products and passage to fixed point algebras by compact group actions with finite Rokhlin dimension preserve the following regularity properties: finite decomposition rank, finite nuclear dimension, and tensorial absorption of the Jiang-Su algebra, the latter in the formulation with commuting towers.

18 pages. This preprint contains the material on crossed products in the first version of arXiv:1407.1277

References in corpus (4)

• Completely positive maps of order zero
• Nuclear dimension and Z-stability
• Trace spaces of simple nuclear C*-algebras with finite-dimensional extreme boundary
• Conjugacy and cocycle conjugacy of automorphisms of ${\mathcal{O}}_2$ are not Borel

Cited by in corpus (6)

• Rokhlin dimension for actions of residually finite groups
• Rokhlin dimension for compact quantum group actions
• Nuclear dimension of crossed products associated to partial dynamical systems
• Strongly outer actions of amenable groups on $\mathcal{Z}$-stable nuclear $C^{\ast }$-algebras
• A categorical perspective on the Atiyah-Segal completion theorem in $\mathrm{KK}$-theory
• Compact Lie group actions with continuous Rokhlin property