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Aperiodic automorphisms of nuclear purely infinite simple $C^{\ast}$-algebras

Published online by Cambridge University Press:  01 December 2000

HIDEKI NAKAMURA
HIDEKI NAKAMURA
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060, Japan (e-mail: h-nakamu@math.sci.hokudai.ac.jp)
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Abstract

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We show that if two aperiodic automorphisms of a separable nuclear unital purely infinite simple $C^{\ast}$-algebra are asymptotically unitarily equivalent, then they are outer conjugate with respect to an automorphism which is isotopic to the identity automorphism. Thus, by Kirchberg and Phillips, they have the same KK-class if and only if they are outer conjugate with respect to an automorphism which is in the KK-class of the identity automorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 6 , December 2000 , pp. 1749 - 1765
Copyright
© 2000 Cambridge University Press