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On the classification of full factors of type III. (English) Zbl 1050.46046
Summary: We introduce a new invariant $$\mathcal{S}(M)$$ 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.

##### MSC:
 46L35 Classifications of $$C^*$$-algebras 46L10 General theory of von Neumann algebras 46L54 Free probability and free operator algebras
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