English

Crossed products by finite group actions with the Rokhlin property

Operator Algebras 2009-02-06 v3

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