An estimate of free entropy and applications

Original · EN

We obtain an estimate of free entropy of generators in a type II₁-factor M which has a subfactor N of finite index with a subalgebra P=P₁P₂⊂N where P₁=R₁'∩P, P₂=R₂'∩P are diffuse, R₁,R₂⊂P are mutually commuting hyperfinite subfactors, and an abelian subalgebra A⊂N such that the correspondence PL²(N,τ)A is M-weakly contained in a subcorrespondence PHA of PL²(M,τ)A, generated by v vectors. The (modified) free entropy dimension of any generating set of M is ≤ 2r+2v+4, where r is the integer part of the index. As a consequence, the interpolated free group subfactors of finite index do not have regular non-prime subfactors or regular diffuse hyperfinite subalgebras.