The Rohlin Property for Actions of Z on UHF Algebras

The Rohlin Property for Z-Actions on UHF Algebras

We define a Rohlin property for Z-actions on UHF algebras and show a non-commutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. We consider two classes of UHF algebras. For UHF algebras in one class including the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebra...

Z-actions on AH algebras and Z-actions on AF algebras

We consider Z-actions (single automorphisms) on a unital simple AH algebra with real rank zero and slow dimension growth and show that the uniform outerness implies the Rohlin property under some technical assumptions. Moreover, two Z-actions with the Rohlin property on such a C∗-algebra are shown to be cocycle conjugate if they are asymptotically unitarily equivalent. We also prove that locall...

Finite Cyclic Group Actions with the Tracial Rokhlin Property

We give examples of actions of Z/2Z on AF algebras and AT algebras which demonstrate the differences between the (strict) Rokhlin property and the tracial Rokhlin property, and between (strict) approximate representability and tracial approximate representability. Specific results include the following. We determine exactly when a product type action of Z/2Z on a UHF algebra has the tracial Rok...

Classification of uniformly outer actions of Z on UHF algebras

We give a complete classification up to cocycle conjugacy of uniformly outer actions of Z on UHF algebras. In particular, it is shown that any two uniformly outer actions of Z on a UHF algebra of infinite type are cocycle conjugate. We also classify them up to outer conjugacy.

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras