Weak amenability of Lie groups made discrete

Abstract

We completely characterize connected Lie groups all of whose countable subgroups are weakly amenable. We also provide a characterization of connected semisimple Lie groups that are weakly amenable. Finally, we show that a connected Lie group is weakly amenable if the group is weakly amenable as a discrete group.

Final version. To appear in Pacific Journal of Mathematics

References in corpus (4)

• Group C*-algebras without the completely bounded approximation property
• Kazhdan and Haagerup Properties in algebraic groups over local fields
• Approximation properties of simple Lie groups made discrete
• Weak amenability and simply connected Lie groups