Crossed products by finite group actions with the Rokhlin property

Details Crossed products by finite group actions with the Rokhlin property Crossed products by finite group actions with the Rokhlin property

2007-04-27

arxiv.org/abs/0704.3651v3

Mathematics

Operator Algebras

22 pages; AMSLaTeX. Changes for version 3: One theorem (on ideals in crossed products by the Rokhlin property) removed; it wil

Scientific paper

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.

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