The Rohlin property for shifts on UHF algebras and automorphisms of Cuntz algebras (Q1923694)

Let \(M_{n^\infty}\) be the infinite tensor product of copies of the \(n\times n\) matrices \(M_n\). The one-sided shift \(\sigma\) on \(M_{n^\infty}\) is defined by \(\sigma(x)= 1_n\otimes x\), \(x\in M_{n^\infty}\), where \(1_n\) is the identity of \(M_n\). The main result of the paper says that this shift has the so-called Rohlin property for any odd \(n\). The author also proves that any automorphism \(\alpha\) of the Cuntz algebra \(O_n\) \((n<\infty)\) has the Rohlin property if \(\alpha^m\) is outer for any \(m\neq 0\).