On Hyperfinite Ii1 Subfactors of Finite Jones Index

We consider certain conditions for abstract lattices of commuting squares, that we prove are necessary and sufficient for them to arise as lattices of higher relative commutants of hyperfinite II1 inclusions of finite Jones index. In particular, we construct a one parameter family of inclusions of hyperfinite II1 factors N ⊂ M, with trivial relative… (More)