2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70520We study the equivalence relation $R_N$ generated by the (non-free) action of the generalized Thompson group $F_N$ on the unit interval. We show that this relation is a standard, quasipreserving ergodic equivalence relation. Using results of Feldman-Moore, Krieger and Connes we prove that the von Neumann algebra $M(R_N)$ associated to $R_N$ is the hyperfinite type $III_λ$ factor, with $λ=1/N$.Operator AlgebrasGroup Theory46L10;37A20text