Crossed products by finite group actions with the Rokhlin property |
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Authors: | Hiroyuki Osaka N. Christopher Phillips |
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Affiliation: | 1. Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan 2. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA
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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: (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. |
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