Commuting squares and the classification of finite depth inclusions of AFD type \(\text{III}_\lambda\) factors, \(\lambda\in(0,1)\) (Q5931091)

Summary: We give a new proof of the classification result due to Sorin Popa that a finite depth inclusion of AFD type \(\text{III}_\lambda\) factors \(N\subset M\), \(\lambda\in (0,1)\), with a common discrete decomposition \(\{N^\infty\subset M^\infty, \theta\}\) is classified, up to isomorphism, by the type II core \(N^\infty\subset M^\infty\) and the standard invariant of \(\theta\).