Groups, Geometry, and Dynamics


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Volume 8, Issue 2, 2014, pp. 375–389
DOI: 10.4171/GGD/230

Published online: 2014-07-08

Finite factor representations of Higman–Thompson groups

Artem Dudko[1] and Konstantin Medynets[2]

(1) Stony Brook University, USA
(2) United States Naval Academy, Annapolis, USA

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.

Keywords: Higman–Thompson groups, essentially free actions, factor representations

Dudko Artem, Medynets Konstantin: Finite factor representations of Higman–Thompson groups. Groups Geom. Dyn. 8 (2014), 375-389. doi: 10.4171/GGD/230