Representation of left centralizers for actions of locally compact quantum groups

TL;DR

This paper extends the representation theorem for locally compact quantum groups to include their actions on von Neumann algebras, broadening the theoretical framework and potential applications in quantum group theory.

Contribution

It generalizes the existing representation theorem to actions of locally compact quantum groups on von Neumann algebras, providing new insights and tools for quantum group analysis.

Findings

Extended the representation theorem to quantum group actions on von Neumann algebras

Revised key results used in the original theorem's proof

Enhanced understanding of quantum group representations

Abstract

We generalize the representation theorem of Junge, Neufang and Ruan [A representation theorem for locally compact quantum groups, Internat. J. Math. 20(3) (2009) 377-400], and some of the important results which were used in its proof, to the case of actions of locally compact quantum groups on von Neumann algebras.