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Zbl 1244.46032
Osaka, Hiroyuki; Phillips, N.Christopher
Crossed products by finite group actions with the Rokhlin property. (English)
[J] Math. Z. 270, No. 1-2, 19-42 (2012). ISSN 0025-5874; ISSN 1432-1823/e

Summary: 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: (a) AI algebras, AT algebras, and related classes characterized by direct limit decompositions using semiprojective building blocks. (b) Simple unital AH algebras with slow dimension growth and real rank zero. (c) C*-algebras with real rank zero or stable rank one. (d) Simple C*-algebras for which the order on projections is determined by traces. (e) C*-algebras whose quotients all satisfy the universal coefficient theorem. (f) C*-algebras with a unique tracial state. 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.

MSC 2000:: *46L55 Noncommutative dynamical systems
46L35 Classifications and factors of C*-algebras

Keywords: crossed products by finite group actions; Rokhlin property; direct limit decompositions

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