# Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 177-195.

Cocycle conjugacy classes of shifts on the hyperfinite II$_1$ factor. II**Authors**: Geoffrey L. Price

**Author institution:**United State Naval Academy, Annapolis, Maryland 21402, U.S.A.

**Summary:**R.T. Powers has constructed a family of unital endomorphisms of the hyperfinite II$_1$ factor $R$, each of which has range a subfactor of index~2, and each of which has no non-trivial invariant subalgebras. A cocycle conjugacy invariant for a Powers shift $\sigma$ is the commutant index, viz., the first index $k$ for which the range of $\sigma$ has non-trivial relative commutant. We show that all of the Powers shifts of commutant index 2 are cocycle conjugate.

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