STRONG SOLIDITY OF FREE ARAKI-WOODS FACTORS

We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III fact...

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Veröffentlicht in:American journal of mathematics 2018-10, Vol.140 (5), p.1231-1252
Hauptverfasser: Boutonnet, Rémi, Houdayer, Cyril, Vaes, Stefaan
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that Shlyakhtenko's free Araki-Woods factors are strongly solid, meaning that for any diffuse amenable von Neumann subalgebra that is the range of a normal conditional expectation, the normalizer remains amenable. This provides the first class of nonamenable strongly solid type III factors.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.2018.0029