Characterization of crossed product (properly infinite case) (Q908489)

Let M be a properly infinite factor with a subfactor N and let E be a normal conditional expectation from M onto N with Index E\(=n\). Put \(N_ 1=IN'I\), where I is the modular conjugation on the standard \(L^ 2\)- space of M. The main result is the following theorem: If \(M\cap N^*=C_ 1\), \(M_ 1\cap N'\) is abelian, and \(\dim_ c(M_ 1\cap N')=n\), then there exist a finite group G (of order n) and an outer action \(\alpha\) of G on N such that M is the crossed product \(N\times_{\alpha}G\). (Furthermore, E is the canonical conditional expectation from \(N\times_{\alpha}G\) onto N).