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

Part of: Selfadjoint operator algebras Ergodic theory

Published online by Cambridge University Press:  29 January 2019

Cyril Houdayer  and
Yusuke Isono
Cyril Houdayer
Affiliation:
Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, CNRS Université Paris-Saclay, 91405 Orsay, FRANCE (cyril.houdayer@math.u-psud.fr)
Yusuke Isono
Affiliation:
RIMS, Kyoto University, 606-8502Kyoto, JAPAN (isono@kurims.kyoto-u.ac.jp)
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Abstract

We investigate factoriality, Connes' type 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 III invariants.

Keywords

amalgamated free product von Neumann algebrasasymptotic centralizerequivalence relationsfullnessPopa's deformation/rigidity theorytype III factorsultraproduct von Neumann algebras

MSC classification

Primary: 46L10: General theory of von Neumann algebras
Secondary: 46L54: Free probability and free operator algebras 46L55: Noncommutative dynamical systems 37A20: Orbit equivalence, cocycles, ergodic equivalence relations 37A40: Nonsingular (and infinite-measure preserving) transformations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 3 , June 2020 , pp. 1495 - 1532
Copyright
Copyright © 2019 The Royal Society of Edinburgh

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