Following an approach of Ozawa, we show that several semidirect products are not weakly amenable. As a consequence, we are able to completely characterize the simply connected Lie groups that are weakly amenable.
"Weak amenability and simply connected Lie groups." Kyoto J. Math. 56 (3) 689 - 700, September 2016. https://doi.org/10.1215/21562261-3600238