Geodesic
Approximation Properties of Simple Lie Groups Made Discrete
Journal of Lie theory, Tome 25 (2015) no. 4, pp. 985-1001
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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.
Classification : 22E46, 22D05, 17B05, 20F65
Mots-clés : Simple Lie groups, approximation properties 
@article{JLT_2015_25_4_JLT_2015_25_4_a2,
     author = {S. Knudby and K. 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/JLT_2015_25_4_JLT_2015_25_4_a2/}
}
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S. Knudby; K. 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/JLT_2015_25_4_JLT_2015_25_4_a2/