Journal of Noncommutative Geometry
Full-Text PDF (245 KB) | Metadata | Table of Contents | JNCG summary
Published online: 2015-10-29
Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental groupArnaud Brothier and Stefaan Vaes (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 [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