Finite factor representations of Higman-Thompson groups. (Q399415)

Summary: We prove that the only finite factor representations of the Higman-Thompson groups \(\{F_{n,r}\}\) and \(\{G_{n,r}\}\) 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.