Crossed products by finite group actions with the Rokhlin property
Abstract
We prove that a number of classes of separable unital C*-algebras are closed under crossed products by finite group actions with the Rokhlin property, including: (1) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (2) Simple unital AH algebras with slow dimension growth and real rank zero. (3) C*-algebras with real rank zero or stable rank one. (4) C*-algebras whose quotients all satisfy the Universal Coefficient Theorem. Along the way, we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective.
Keywords
Cite
@article{arxiv.0704.3651,
title = {Crossed products by finite group actions with the Rokhlin property},
author = {Hiroyuki Osaka and N. Christopher Phillips},
journal= {arXiv preprint arXiv:0704.3651},
year = {2009}
}
Comments
22 pages; AMSLaTeX. Changes for version 3: One theorem (on ideals in crossed products by the Rokhlin property) removed; it will appear in a different paper. Minor improvements. Changes for version 2: Substantial expansion