JournalsggdVol. 8, No. 2pp. 375–389

Finite factor representations of Higman–Thompson groups

  • Artem Dudko

    Stony Brook University, USA
  • Konstantin Medynets

    United States Naval Academy, Annapolis, USA
Finite factor representations of Higman–Thompson groups cover
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Abstract

We prove that the only finite factor representations of the Higman–Thompson groups {Fn,r}\{F_{n,r}\} and {Gn,r}\{G_{n,r}\} 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

DOI 10.4171/GGD/230