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

Dorin Dutkay·Gabriel Picioroaga
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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 $III_λ$ factor, with $λ=1/N$.

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Dorin Dutkay, Gabriel Picioroaga. 2004-09-11. The von Neumann Algebra of the Canonical Equivalence Relation of the Generalized Thompson Group. https://arxiv.org/abs/math/0403332

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