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

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

2004-03-22

arxiv.org/abs/math/0403332v5

Mathematics

Operator Algebras

Scientific paper

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 $III_{\lambda}$ factor, with $\lambda=1/N$.

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