Abstract
Constructing non-commutative Bernoulli shifts one starts with a measure theoretic Bernoulli shift and an equivalence relation on the measure space. There is a doubly infinite increasing sequence of measure preserving ergodic equivalence relations giving an increasing sequence of pairwise isomorphic von Neumann algebras invariant under the Bernoulli shift automorphism. We consider the index of Jones for those subalgebras and give an explicit example of conjugate non-commutative Bernoulli shifts.
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