We prove that the only finite factor representations of the Higman–Thompson groups {Fn,r} and {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 the commutator subgroup of a Higman–Thompson group must be essentially free. Finite factor representations of other classes of groups are also discussed.
1
Stony Brook University, USA
2
United States Naval Academy, Annapolis, USA
Artem Dudko; Konstantin Medynets. Finite factor representations of Higman–Thompson groups. Groups, geometry, and dynamics, Tome 8 (2014) no. 2, pp. 375-389. doi: 10.4171/ggd/230
@article{10_4171_ggd_230,
author = {Artem Dudko and Konstantin Medynets},
title = {Finite factor representations of {Higman{\textendash}Thompson} groups},
journal = {Groups, geometry, and dynamics},
pages = {375--389},
year = {2014},
volume = {8},
number = {2},
doi = {10.4171/ggd/230},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/230/}
}
TY - JOUR
AU - Artem Dudko
AU - Konstantin Medynets
TI - Finite factor representations of Higman–Thompson groups
JO - Groups, geometry, and dynamics
PY - 2014
SP - 375
EP - 389
VL - 8
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/230/
DO - 10.4171/ggd/230
ID - 10_4171_ggd_230
ER -
%0 Journal Article
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%A Konstantin Medynets
%T Finite factor representations of Higman–Thompson groups
%J Groups, geometry, and dynamics
%D 2014
%P 375-389
%V 8
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/230/
%R 10.4171/ggd/230
%F 10_4171_ggd_230
