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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 inductive limits of II$ _{1}$ factors with spectral gap


Author: Sorin Popa
Journal: Trans. Amer. Math. Soc. 364 (2012), 2987-3000
MSC (2010): Primary 46L10, 46L37
Published electronically: January 26, 2012
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Abstract: We consider II$ _{1}$ factors $ M$ which can be realized as inductive limits of subfactors, $ N_{n} \nearrow M$, having spectral gap in $ M$ and satisfying the bi-commutant condition $ (N_{n}'\cap M)'\cap M=N_{n}$. Examples are the enveloping algebras associated to non-Gamma subfactors of finite depth, as well as certain crossed products of McDuff factors by amenable groups. We use deformation/rigidity theory to obtain classification results for such factors.


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Additional Information

Sorin Popa
Affiliation: Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095-155505
Email: popa@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05389-X
PII: S 0002-9947(2012)05389-X
Received by editor(s): October 18, 2009
Received by editor(s) in revised form: June 3, 2010
Published electronically: January 26, 2012
Additional Notes: This work was supported in part by NSF Grant 0601082.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.