  In this paper 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.
