On the classification of inductive limits of II${}_1$ factors with spectral gap

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 $(N_n^{\prime }\cap M{)}^{\prime }\cap M=N_n$. 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 techniques to obtain classification results for such factors.

14 pages

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