We introduce notions of the Rohlin property and the approximate
representability for inclusions of unital Cβ-algebras. We investigate a dual
relation between the Rohlin property and the approximate representability. We
prove that a number of classes of unital Cβ-algebras are closed under
inclusions with the Rohlin property, including:
AF algebras, AI algebras, AT algebras, and related classes characterized by
direct limit decomposition using semiprojective building blocks. Cβ-algebras
with stable rank one. Cβ-algebras with real rank zero.Comment: We revised the section 4 and its correspondent part in Introduction
in the original pape