2012/09/18 by N. Christopher Phillips, Phillips, N. Christopher · 1 citation
Mathematics · #46L #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1209.3859
openalex publication_date 2012/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove several results of the following general form: automorphisms of (or actions of ℤd on) certain kinds of simple separable unital C*-algebras A which have a suitable version of the Rokhlin property are generic among all automorphisms (or actions), or in a suitable class of automorphisms. That is, the ones with the version of the Rokhlin property contain a dense Gδ-subset of the set of all such automorphisms (or actions). Specifically, we prove the following. If A is stable under tensoring with the Jiang-Su algebra Z, and has tracial rank zero, then automorphisms with the tracial Rokhlin property are generic. If A has tracial rank zero, or, more generally, A is tracially approximately divisible together with a technical condition, then automorphisms with the tracial Rokhlin property are generic among the approximately inner automorphisms. If A is stable under tensoring with the Cuntz algebra O∞ or with a UHF algebra of infinite type, then actions of ℤd on A with the Rokhlin property are generic among all actions of ℤd. We further give a related but more restricted result for actions of finite groups.