A 1-cohomology characterization of property (T) in von Neumann algebras

TL;DR

This paper characterizes property (T) for von Neumann algebras using 1-cohomology, extending the analogy of the Delorme-Guichardet Theorem from group theory to operator algebras.

Contribution

It provides a novel cohomological criterion for property (T) in von Neumann algebras, bridging group cohomology and operator algebra theory.

Findings

Property (T) characterized by 1-cohomology

Extension of Delorme-Guichardet Theorem to von Neumann algebras

New tools for analyzing rigidity in operator algebras

Abstract

We obtain a characterization of property (T) for von Neumann algebras in terms of 1-cohomology similar to the Delorme-Guichardet Theorem for groups.