Weak amenability of Lie groups made discrete

Søren Knudby

Vol. 297 (2018), No. 1, 101–116

DOI: 10.2140/pjm.2018.297.101

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.

Keywords

weak amenability, Lie groups, locally compact groups

Mathematical Subject Classification 2010

Primary: 22E15, 22E40, 43A22, 43A80

Milestones

Received: 13 December 2016

Revised: 15 April 2017

Accepted: 9 January 2018

Published: 7 October 2018