Von Neumann Modules, Intertwiners and Self-Duality

TL;DR

This paper presents a simplified, self-contained proof of the self-duality property of von Neumann modules by utilizing the intertwiner space approach for representations of the commutant algebra.

Contribution

It introduces a new, streamlined proof of self-duality for von Neumann modules based on the intertwiner space framework, simplifying previous methods.

Findings

Provides a simpler proof of self-duality for von Neumann modules

Utilizes the intertwiner space approach for representations of the commutant algebra

Streamlines the theoretical understanding of von Neumann modules

Abstract

We apply the ideas of Muhly, Skeide and Solel [MSS03] of considering von Neumann B-modules as intertwiner spaces for representations of B' to obtain a new, simple and self-contained proof for self-duality of von Neumann modules. This simplifies also the approach of [MSS03].