Examples of Amenable Kac system

TL;DR

This paper characterizes amenable Kac systems using one-dimensional representations and demonstrates that bicrossproducts of amenable groups are both amenable and coamenable.

Contribution

It provides a new characterization of amenable Kac systems and simplifies the proof that bicrossproducts of amenable groups are also amenable and coamenable.

Findings

Characterization of amenable Kac systems via one-dimensional representations

Bicrossproducts of amenable groups are both amenable and coamenable

Simplified proof of bicrossproduct properties

Abstract

By giving an interesting characterisation of amenable multiplicative unitaries in term of one dimensional representations, we show in a simple way that bicrossproducts of amenable locally compact groups is both amenable and coamenable.