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The one-cocycle property for shifts
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Description
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.
Journal
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- Ergodic Theory and Dynamical Systems
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Ergodic Theory and Dynamical Systems 25 823-859, 2005
Cambridge University Press
