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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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