Abstract
When A is a unital simple AF C ∗ -algebra and has a unique tracial state, it is shown that the crossed product of the two-sided infinite tensor product ⊗ Z A by the shift is a tracially AF C ∗ -algebra. A similar result is given to the crossed product of a certain non-unital two-sided infinite tensor product by the shift. Applying a far-reaching classification result of such C ∗ -algebras by H. Lin, we obtain an example of a one-parameter automorphism group on some AF C ∗ -algebra which is not approximately inner, a counter-example to the AF version of the so-called Powers–Sakai conjecture [23].
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