A structural result of irreducible inclusions of type IIIa FACTORS, λ ∈ (0,1)

Phan H. Loi, Wright State University


Given an irreducible inclusion of factors with finite index N ⊂ M, where M is of type IIIλ1/m, N of type IIIλ1/n,0 < λ < 1, and m,n are relatively prime positive integers, we will prove that if N ⊂ M satisfies a commuting square condition, then its structure can be characterized by using fixed point algebras and crossed products of automorphisms acting on the middle inclusion of factors associated with N ⊂ M. Relations between N ⊂ M and a certain G-kernel on subfactors are also discussed. © 1998 American Mathematical Society.