The Rohlin property for shifts of finite type (Q2583793)

The noncommutative version of the classical Rohlin property in ergodic theory plays an important role in the classification of \(C^*\)-algebras. This article discusses and clarifies briefly some of the quite technical definitions in the literature. It is then proved that, for unital AF-algebras, the approximate Rohlin property implies the Rohlin property. This result has previously been shown by \textit{A.~Kishimoto} under some further \(K\)-theoretical assumptions [J.\ Reine Angew.\ Math.\ 465, 183--196 (1995; Zbl 0824.46070)]. Generalisations of this result for non-AF algebras are also briefly discussed. As an application, it is proved that the shift automorphism on the bilateral AF-algebra associated to an aperiodic irreducible subshift of finite type has the Rohlin property.