Continuous families of hyperfinite subfactors with the same standard invariant

Dietmar Bisch; Remus Nicoara; Sorin Popa

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Continuous families of hyperfinite subfactors with the same standard invariant

Dietmar Bisch·Remus Nicoara·Sorin Popa

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Abstract

We construct numerous continuous families of irreducible subfactors of the hyperfinite II$_1$ factor, which are non-isomorphic, but have all the same standard invariant. In particular, we obtain 1-parameter families of irreducible, non-isomorphic subfactors of the hyperfinite II$_1$ factor, which have Jones index 6 and have all the same standard invariant with property (T). We exploit the fact that property (T) groups have uncountably many non-cocycle conjugate cocycle actions on the hyperfinite II$_1$ factor.

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Dietmar Bisch, Remus Nicoara, Sorin Popa. 2006-06-06. Continuous families of hyperfinite subfactors with the same standard invariant. https://arxiv.org/abs/math/0604460

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