JournalsggdVol. 14, No. 3pp. 837–855

Representing interpolated free group factors as group factors

  • Sorin Popa

    University of California Los Angeles, USA
  • Dimitri L. Shlyakhtenko

    University of California Los Angeles, USA
Representing interpolated free group factors as group factors cover
Download PDF

A subscription is required to access this article.

Abstract

We construct a one parameter family of ICC groups {Gt}t>1\{G_t\}_{t > 1}, with the property that the group factor L(Gt)L(G_t) is isomorphic to the interpolated free group factor L(Ft):=L(F2)1/t1L(\mathbb F_t):=L(\mathbb{F}_2)^{1/\sqrt{t-1}}, for all tt. Moreover, the groups GtG_t have fixed cost tt, are strongly treeable and freely generate any treeable ergodic equivalence relation of same cost.

Cite this article

Sorin Popa, Dimitri L. Shlyakhtenko, Representing interpolated free group factors as group factors. Groups Geom. Dyn. 14 (2020), no. 3, pp. 837–855

DOI 10.4171/GGD/565