Journal of Lie Theory 25 (2015), No. 4, 985--1001
Copyright Heldermann Verlag 2015
Approximation Properties of Simple Lie Groups Made Discrete
Sören Knudby
Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
knudby@math.ku.dk
Kang Li
Dept. of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
kang.li@math.ku.dk
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.
Keywords: Simple Lie groups, approximation properties.
MSC: 22E46, 22D05, 17B05, 20F65
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