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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the classification of full factors of type III


Author: Dimitri Shlyakhtenko
Journal: Trans. Amer. Math. Soc. 356 (2004), 4143-4159
MSC (2000): Primary 46L10; Secondary 46L54
Published electronically: April 16, 2004
MathSciNet review: 2058841
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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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Additional Information

Dimitri Shlyakhtenko
Affiliation: Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095
Email: shlyakht@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-04-03457-9
PII: S 0002-9947(04)03457-9
Received by editor(s): July 21, 2002
Received by editor(s) in revised form: July 17, 2003
Published electronically: April 16, 2004
Article copyright: © Copyright 2004 American Mathematical Society