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

2009/10/13 by Popa, Sorin
#46L10 #46L37 #46L40 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.0910.2241

Abstract

We consider II₁ 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'∩ M)'∩ 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.

Related

• On spectral gap rigidity and Connes invariant χ(M)
• Spectral gap characterization of full type III factors
• A characterization of depth 2 subfactors of II₁ factors
• Fullness and Connes' \boldsymbolτ invariant of type III tensor product factors
• Intermediate Subfactors with No Extra Structure