We prove that the only finite factor representations of the Higman–Thompson groups and are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of the commutator subgroup of a Higman–Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.
Cite this article
Artem Dudko, Konstantin Medynets, Finite factor representations of Higman–Thompson groups. Groups Geom. Dyn. 8 (2014), no. 2, pp. 375–389