Finite Factor Representations of Higman-Thompson groups

  title={Finite Factor Representations of Higman-Thompson groups},
  author={Artem Dudko and Konstantin Medynets},
We prove that the only finite factor-representations of the HigmanThompson groups {Fn,r}, {Gn,r} are the regular representations and scalar representations arising from group abelianizations. As a corollary, we obtain that any measure-preserving ergodic action of a simple Higman-Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.