Kishimoto, Akitaka The Rohlin property for shifts on UHF algebras and automorphisms of Cuntz algebras. (English) Zbl 0902.46031 J. Funct. Anal. 140, No. 1, 100-123 (1996). 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 \(m\neq 0\). Reviewer: Kh.N.Boyadzhiev (Ada) Cited in 2 ReviewsCited in 44 Documents MSC: 46L05 General theory of \(C^*\)-algebras 46L55 Noncommutative dynamical systems 46L40 Automorphisms of selfadjoint operator algebras Keywords:UHF algebras; infinite tensor product; one-sided shift; Rohlin property; automorphism; Cuntz algebra PDFBibTeX XMLCite \textit{A. Kishimoto}, J. Funct. Anal. 140, No. 1, 100--123 (1996; Zbl 0902.46031) Full Text: DOI