Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras

TL;DR

This paper studies the structural properties of amalgamated free product von Neumann algebras, focusing on factoriality, Connes' type III invariants, and fullness, using Popa's deformation/rigidity theory to generalize previous results and provide new examples.

Contribution

It generalizes existing structural results and constructs new full amalgamated free product factors with explicitly computed Connes' type III invariants.

Findings

Generalized structural results on amalgamated free product von Neumann algebras

Constructed new examples of full factors with known Connes' invariants

Extended the understanding of factoriality and fullness in this context

Abstract

We investigate factoriality, Connes' type ${\rm III}$ invariants and fullness of arbitrary amalgamated free product von Neumann algebras using Popa's deformation/rigidity theory. Among other things, we generalize many previous structural results on amalgamated free product von Neumann algebras and we obtain new examples of full amalgamated free product factors for which we can explicitely compute Connes' type ${\rm III}$ invariants.