open access

https://hdl.handle.net/2115/5907

The one-cocycle property for shifts

英語

2005

Cambridge University Press

Ergodic Theory and Dynamical Systems

25

823-859

The two-sided shift on the infinite tensor product of copies of the n × n matrix algebra has the so-called Rohlin property, which entails the one-cocycle property, useful in analyzing cocycle-conjugacy classes. In the case n = 2, the restriction of the shift to the gauge-invariant CAR algebra also has the one-cocycle property. We extend the latter result to an arbitrary n ≥ 2. As a corollary it follows that the flow α on the Cuntz algebra On = C*(s0, s1, . . . , sn−1) defined by αt (sj ) = eipj t sj has the Rohlin property (for flows) if and only if p0, . . . ,pn−1 generate R as a closed sub-semigroup. Note that then such flows are all cocycle-conjugate to each other.

学術雑誌論文

Version of Record

Copyright © 2005 Cambridge University Press

0143-3857