Construction of a canonical subfactor for an inclusion of factors with a common Cartan sub\-algebra (Q1409283)

It is shown that, for, any inclusion of (separable) factors \(N \subseteq M\) of finite Jones index possessing a common Cartan subalgebra, there exists a subfactor \(L\) of \(N\), an outer action \(\beta\) of a finite group \(G\) on \(L\) and a subgroup \(H\) of \(G\) such that (\(N \subseteq M\)) is isomorphic to (\(L \rtimes_\beta H \subseteq L \rtimes_\beta G\)). The authors given an application of the result stated above concerning a minimal action of a finite-dimensional Kac algebra on a factor.