On the classification of inductive limits of II₁ factors with spectral gap

Popa, Sorin

doi:10.1090/S0002-9947-2012-05389-X

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