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arXiv:math/0403332 [math.OA]AbstractReferencesReviewsResources

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

Dorin Dutkay, Gabriel Picioroaga

Published 2004-03-22, updated 2004-09-11Version 5

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 $\lambda=1/N$.

Categories: math.OA, math.GR
Subjects: 46L10, 37A20
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