### Abstract

Let G be an inductive limit of finite cyclic groups, and A be a unital simple projectionless C*-algebra with K_{1}(A) ≅ G and a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we show that any two aperiodic elements in Aut(A)/WInn(A) are conjugate, where WInn(A) means the subgroup of Aut(A) consisting of automorphisms which are inner in the tracial representation. In the second part of this paper, we consider a class of unital simple C*-algebras with a unique tracial state which contains the class of unital simple A-algebras of real rank zero with a unique tracial state. This class is closed under inductive limits and crossed products by actions of with the Rohlin property. Let A be a TAF-algebra in this class. We show that for any automorphism α of A there exists an automorphism of A with the Rohlin property such that ∼ α and α are asymptotically unitarily equivalent. For the proof we use an aperiodic automorphism of the Jiang-Su algebra.

Original language | English |
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Pages (from-to) | 1233-1261 |

Number of pages | 29 |

Journal | International Journal of Mathematics |

Volume | 20 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2009 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)