SHIFTS ON THE HYPERFINITE PI(1) FACTOR

Powers has constructed a family of unital endomorphisms of the hyperfi nite II1 factor R. The range of each Powers shift sigma is a subfactor of index 2 in R. A cocycle conjugacy invariant for a Powers shift is its commutant index, i.e., the first index k for which the range of si gma(k) has a nontrivial relative commutant in R. Previously we have sh own that all Powers shifts of commutant index 2 are cocycle conjugate. In this paper results are obtained on the classification of the cocyc le conjugacy classes of Powers shifts of higher commutant index. (C) 1 998 Academic Press.