A note on amenability of locally compact quantum groups

TL;DR

This paper introduces quantum injectivity as a new concept and proves its equivalence to the dual's amenability, offering a novel characterization of amenability in locally compact groups.

Contribution

It defines quantum injectivity and establishes its equivalence to dual amenability, providing a new perspective on group amenability.

Findings

Quantum injectivity is equivalent to dual amenability.

Provides a new characterization of amenability for locally compact groups.

Establishes a link between quantum group properties and classical group theory.

Abstract

In this short note we introduce a notion called "quantum injectivity" of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of locally compact groups.