We consider the class of connected simple Lie groups equipped with the discrete topology. We show that within this class of groups the following approximation properties are equivalent: (1) the Haagerup property; (2) weak amenability; (3) the weak Haagerup property. In order to obtain the above result we prove that the discrete group GL(2,K) is weakly amenable with constant 1 for any field K.
1
Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
Sören Knudby; Kang Li. Approximation Properties of Simple Lie Groups Made Discrete. Journal of Lie Theory, Tome 25 (2015) no. 4, pp. 985-1001. http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a2/
@article{JOLT_2015_25_4_a2,
author = {S\"oren Knudby and Kang Li},
title = {Approximation {Properties} of {Simple} {Lie} {Groups} {Made} {Discrete}},
journal = {Journal of Lie Theory},
pages = {985--1001},
year = {2015},
volume = {25},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a2/}
}
TY - JOUR
AU - Sören Knudby
AU - Kang Li
TI - Approximation Properties of Simple Lie Groups Made Discrete
JO - Journal of Lie Theory
PY - 2015
SP - 985
EP - 1001
VL - 25
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a2/
ID - JOLT_2015_25_4_a2
ER -
%0 Journal Article
%A Sören Knudby
%A Kang Li
%T Approximation Properties of Simple Lie Groups Made Discrete
%J Journal of Lie Theory
%D 2015
%P 985-1001
%V 25
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2015_25_4_a2/
%F JOLT_2015_25_4_a2
