Lattices of intermediate subfactors (Q1923962)

The author studies the lattice structure of intermediate subfactors. Let \(N\) be a subfactor of a type \(\text{II}_1\) factor \(M\) and let the Jones index \([M:N]\) be finite. It is shown that if \(M\cap N'= \mathbb{C}\), then the intermediate subfactor lattice \(\text{Lat}(N\subset M)\) is a finite set. The author also investigates the finite lattices with at most six elements to determine which of them can be realized as intermediate subfactor lattices. He proves that such a realization exists for the lattices with at most five elements.