Square-integrable coactions of locally compact quantum groups

TL;DR

This paper introduces and analyzes square-integrable coactions of locally compact quantum groups on Hilbert modules, extending classical results and providing a generalized Kasparov Stabilisation Theorem for quantum group actions.

Contribution

It generalizes the concept of square-integrability to quantum group coactions on Hilbert modules and proves an equivariant Kasparov Stabilisation Theorem.

Findings

Established a framework for square-integrable coactions of quantum groups

Extended Kasparov's Stabilisation Theorem to the quantum setting

Connected square-integrability with corepresentations and coactions on C*-algebras

Abstract

We define and study square-integrable coactions of locally compact quantum groups on Hilbert modules, generalising previous work for group actions. As special cases, we consider square-integrable Hilbert space corepresentations and integrable coactions on C*-algebras. Our main result is an equivariant generalisation of Kasparov's Stabilisation Theorem.