
Journal of Lie Theory 25 (2015), No. 4, 9851001 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 [ Fulltextpdf (348 KB)] for subscribers only. 