An Estimate of Free Entropy and Applications
نویسنده
چکیده
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 = P1∨P2 ⊂ 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 PL 2(N , τ)A is M-weakly contained in a subcorrespondence PHA of PL 2(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.
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