Commuting Squares and the Classification of Finite Depth Inclusions of AFD Type III_λ Factors, λ ∈ (0, 1)

Abstract

We give a new proof of the classification result due to Sorm Popa that a finite depth inclusion of AFD type IIIλ factors N ⊂ _M_Al, λ ∈ (0, 1), with a common discrete decomposition {_N_∞ ⊂ _M_∞, θ} is classified, up to isomorphism, by the type II core i>N∞ ⊂ _M_∞ and the standard invariant of θ.