Representing interpolated free group factors as group factors (Q2032438)

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