Inclusion of type III factors constructed from ergodic flows (Q912364)

The main result in this paper is the following: Let \((F_ t,Y)\), \((S_ t,Z)\) be conservative ergodic flows. Assume that a flow \((T_ t,X)\) is a common finite extension of \((F_ t,Y)\) and \((S_ t,Z)\). Then one can construct factors M, N of type III with \(M\geq N\) and a normal expectation from M onto N with finite index such that \((F_ t,Y)\), \((S_ t,Z)\) are the flows of weights of M and N respectively. This is a converse of a result in Proc. Japan Acad., Ser. A 64, 11-13 (1988; Zbl 0643.46044) by the same authors.