Abstract
We define a Rohlin property for one-parameter automorphism groups of unital simpleC *-algebras and show that for such an automorphism group any cocycle is almost a coboundary. We apply the same method to the single automorphism case and show that if an automorphism of a unital simpleC *-algebra with a certain condition has a central sequence of approximate eigen-unitaries for any complex number of modulus one, then any cocycle is almost a coboundary, or the automorphism has the stability. We also show that if a one-parameter automorphism group of a unital separable purely infinite simpleC *-algebra has the Rohlin property then the crossed product is simple and purely infinite.
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Communicated by H. Araki
Dedicated to: Prof. H. Hasegawa
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Kishimoto, A. A Rohlin property for one-parameter automorphism groups. Commun.Math. Phys. 179, 599–622 (1996). https://doi.org/10.1007/BF02100099
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DOI: https://doi.org/10.1007/BF02100099