The Rohlin Property for Actions of Z² on UHF Algebras

الأصل · EN

We define a Rohlin property for actions of Z² on UHF algebras and show a noncommutative Rohlin type theorem. Among those actions with the Rohlin property, we classify product type actions up to outer conjugacy. In particular we present two classes of UHF algebras. For UHF algebras in one class, which includes the CAR algebra, there is one and only one outer conjugacy class of product type actions and for UHF algebras in the other class, contrary to the case of actions of Z, there are infinitely many outer conjugacy classesof product type actions.