The von Neumann Algebra of the Canonical Equivalence Relation of the Generalized Thompson Group

Dorin Dutkay; Gabriel Picioroaga

paper

The von Neumann Algebra of the Canonical Equivalence Relation of the Generalized Thompson Group

arXiv:math/0403332

Abstract

We 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 $I I I_{λ}$ factor, with $λ = 1/ N$ .

Cited by in corpus (1)

Triangle Joins of SP1 Equivalence Relations and their Cost