A Rohlin Property for One-parameter Automorphism Groups of the Hyperfinite ${\mathrm{II}}_1$ Factor

Abstract

We first define a Rohlin property for one-parameter automorphism groups of the hyperfinite type ${\mathrm{II}}_1$ factor as an analogue of Kishimoto's definition for one-parameter automorphism groups of unital simple ${\mathrm{C}}^{\ast }$-algebras.

Secondly, we prove equivalence between the Rohlin property and the cohomology vanishing in an appropriate central sequence algebra, which is a variation of Kishimoto's theorem in ${\mathrm{C}}^{\ast }$-algebra theory.