We construct first examples of non-trivial groups without non-cyclic free subgroups whose reduced C∗-algebra is simple and has unique trace. This answers a question of de la Harpe. Both torsion and torsion free examples are provided. In particular, we show that the reduced C∗-algebra of the free Burnside group B(m,n) of rank m≥2 and any sufficiently large odd exponent n is simple and has unique trace.
Alexander Yu. Olshanskii; Denis Osin. $C$*-simple groups without free subgroups. Groups, geometry, and dynamics, Tome 8 (2014) no. 3, pp. 933-983. doi: 10.4171/ggd/253
@article{10_4171_ggd_253,
author = {Alexander Yu. Olshanskii and Denis Osin},
title = {$C$*-simple groups without free subgroups},
journal = {Groups, geometry, and dynamics},
pages = {933--983},
year = {2014},
volume = {8},
number = {3},
doi = {10.4171/ggd/253},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/253/}
}
TY - JOUR
AU - Alexander Yu. Olshanskii
AU - Denis Osin
TI - $C$*-simple groups without free subgroups
JO - Groups, geometry, and dynamics
PY - 2014
SP - 933
EP - 983
VL - 8
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/253/
DO - 10.4171/ggd/253
ID - 10_4171_ggd_253
ER -
%0 Journal Article
%A Alexander Yu. Olshanskii
%A Denis Osin
%T $C$*-simple groups without free subgroups
%J Groups, geometry, and dynamics
%D 2014
%P 933-983
%V 8
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/253/
%R 10.4171/ggd/253
%F 10_4171_ggd_253
