Journal of Noncommutative Geometry


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Volume 9, Issue 3, 2015, pp. 775–796
DOI: 10.4171/JNCG/207

Published online: 2015-10-29

Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group

Arnaud Brothier[1] and Stefaan Vaes[2]

(1) Vanderbilt University, Nashville, USA
(2) Katholieke Universiteit Leuven, Belgium

We construct irreducible hyperfinite subfactors of index 6 with a prescribed fundamental group from a large family containing all countable and many uncountable subgroups of $\mathbb R_+$. We also prove that there are unclassifiably many irreducible hyperfinite group-type subfactors of index 6 that all have the same standard invariant. More precisely, we associate such a subfactor to every ergodic measure preserving automorphism of the interval Œ[0; 1] and prove that the resulting subfactors are isomorphic if and only if the automorphisms are conjugate.

Keywords: Subfactor, standard invariant, von Neumann algebra, deformation/rigidity theory

Brothier Arnaud, Vaes Stefaan: Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group. J. Noncommut. Geom. 9 (2015), 775-796. doi: 10.4171/JNCG/207