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

  • Arnaud Brothier

    Vanderbilt University, Nashville, USA
  • Stefaan Vaes

    Katholieke Universiteit Leuven, Belgium

Abstract

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 . 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.

Cite this article

Arnaud Brothier, Stefaan Vaes, Families of hyperfinite subfactors with the same standard invariant and prescribed fundamental group. J. Noncommut. Geom. 9 (2015), no. 3, pp. 775–796

DOI 10.4171/JNCG/207