Continuous families of hyperfinite subfactors with the same standard invariant

2006/04/21 by Bisch, Dietmar, Nicoara, Remus, Popa, Sorin
#46L10 #46L37 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.math/0604460

Abstract

We construct numerous continuous families of irreducible subfactors of the hyperfinite II₁ factor, which are non-isomorphic, but have all the same standard invariant. In particular, we obtain 1-parameter families of irreducible, non-isomorphic subfactors of the hyperfinite II₁ factor, which have Jones index 6 and have all the same standard invariant with property (T). We exploit the fact that property (T) groups have uncountably many non-cocycle conjugate cocycle actions on the hyperfinite II₁ factor.

Related

• New hyperfinite subfactors with infinite depth
• Examples of subfactors with property T standard invariant
• Forked Temperley-Lieb Algebras and Intermediate Subfactors
• Non-embeddable II₁ factors resembling the hyperfinite II₁ factor
• Subfactors of free products of rescalings of a II₁-factor