Subfactors of an Approximately Finite Dimensional Factor of Type II₁

Abstract

In this last chapter of the volume, we will study the structure of subfactors of a factor. In the classical theory of abstract algebra, simple subalgebras of a centrally simple algebra with finite dimension over the center are described by the Galois group of the pair. In the case of subfactors of a factor, it turns out that the concept of group is not enough to describe the structure of the pair. Of course, a group of automorphisms of a factor gives rise to a von Neumann subalgebra as the fixed point subalgebra. But, we will see that there are much more interesting subfactors which does not correspond to any kind of groups.