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Crossed products by finite group actions with the Rokhlin property

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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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Authors and Affiliations

  1. Department of Mathematical Sciences, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan

    Hiroyuki Osaka

  2. Department of Mathematics, University of Oregon, Eugene, OR, 97403-1222, USA

    N. Christopher Phillips

Authors
  1. Hiroyuki Osaka
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  2. N. Christopher Phillips
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Correspondence to N. Christopher Phillips.

Additional information

Research of H. Osaka partially supported by The Open Research Center Project for Private Universities: matching fund from MEXT, 2004-2008. Research of N. Christopher Phillips partially supported by NSF grants DMS 0302401 and DMS 0701076.

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Osaka, H., Phillips, N.C. Crossed products by finite group actions with the Rokhlin property. Math. Z. 270, 19–42 (2012). https://doi.org/10.1007/s00209-010-0784-4

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