## Journal of the Mathematical Society of Japan

### The Rohlin property for $Z^{2}$-actions on UHF algebras

Hideki NAKAMURA

#### Abstract

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

#### Article information

Source
J. Math. Soc. Japan, Volume 51, Number 3 (1999), 583-612.

Dates
First available in Project Euclid: 10 June 2008

https://projecteuclid.org/euclid.jmsj/1213107906

Digital Object Identifier
doi:10.2969/jmsj/05130583

Mathematical Reviews number (MathSciNet)
MR1691489

Zentralblatt MATH identifier
0947.46044

#### Citation

NAKAMURA, Hideki. The Rohlin property for $Z^{2}$ -actions on UHF algebras. J. Math. Soc. Japan 51 (1999), no. 3, 583--612. doi:10.2969/jmsj/05130583. https://projecteuclid.org/euclid.jmsj/1213107906