The Rohlin property for Z²-actions on UHF algebras

Abstract

We define a Rohlin property for Z²-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 algebras in the other class, contrary to the case of Z-actions, there are infinitely many outer conjugacy classes of product type actions.