Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras

TL;DR

This paper investigates how locally compact quantum groups act on von Neumann algebras, focusing on amenability and Reiter's conditions, with applications to specific representations and corepresentations.

Contribution

It introduces Reiter's conditions for quantum group actions on von Neumann algebras and explores their implications for amenability and specific representations.

Findings

Reiter's conditions characterize amenability of quantum group actions.

Applications include analysis of actions related to certain representations.

Provides new criteria for amenability in the quantum setting.

Abstract

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented.