The Rohlin Property for Actions of $Z^{2}$ on UHF Algebras

Details The Rohlin Property for Actions of $Z^{2}$ on UHF Algebras The Rohlin Property for Actions of $Z^{2}$ on UHF Algebras

1996-10-09

arxiv.org/abs/funct-an/9610001v2

Mathematics

Operator Algebras

35 pages, no figure, LaTex. Changes suggested by the referee are made. To appear in Journal of the Mathematical Society of Jap

Scientific paper

We define a Rohlin property for actions of $Z^{2}$ 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.

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