A metric characterization of freeness

Léonard Cadilhac, Benoit Collins

Let $\mathcal{M}$ be a finite von Neumann algebra and $u_1,\dots ,u_N$ be unitaries in $\mathcal{M}$. We show that $u_1,\dots ,u_N$ freely generate $L({\mathbb{F}}_N)$ if and only if $…