On the classification of full factors of type III

Shlyakhtenko, Dimitri

doi:10.1090/S0002-9947-04-03457-9

On the classification of full factors of type III
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Trans. Amer. Math. Soc. 356 (2004), 4143-4159 Request permission

Abstract:

We introduce a new invariant $\mathscr {S}(M)$ for type III factors $M$ with no almost-periodic weights. We compute this invariant for certain free Araki-Woods factors. We show that Connes’ invariant $\tau$ cannot distinguish all isomorphism classes of free Araki-Woods factors. We show that there exists a continuum of mutually non-isomorphic free Araki-Woods factors, each without almost-periodic weights.

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