Weak amenability and simply connected Lie groups

TL;DR

This paper investigates the weak amenability of certain Lie groups, demonstrating non-weak amenability for some semidirect products and characterizing which simply connected Lie groups possess this property.

Contribution

It introduces a new characterization of weakly amenable simply connected Lie groups and applies Ozawa's approach to identify non-weakly amenable semidirect products.

Findings

Several semidirect products are not weakly amenable

Characterization of weakly amenable simply connected Lie groups

Extension of Ozawa's approach to Lie group analysis

Abstract

Following an approach of Ozawa, we show that several semidirect products are not weakly amenable. As a consequence, we are able to characterize the simply connected Lie groups that are weakly amenable.