2004/02/07 by Marius Stefan, Stefan, Marius
Mathematics · #46Lxx (Primary) 47Lxx (Secondary) #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46Lxx #msc:47Lxx
paper · pdf · doi:10.48550/arxiv.math/0402109
arxiv created 2004/02/07 · arxiv updated 2009/12/01
We obtain an estimate of free entropy of generators in a type II1-factor \mcM which has a subfactor \mcN of finite index with a subalgebra \mcP=\mcP1\vee\mcP2⊂\mcN where \mcP1=\mcR1'∩\mcP, \mcP2=\mcR2'∩\mcP are diffuse, \mcR1,\mcR2⊂\mcP are mutually commuting hyperfinite subfactors, and an abelian subalgebra \mcA⊂\mcN such that the correspondence _\mcPL2(\mcN,τ)_\mcA is \mcM-weakly contained in a subcorrespondence _\mcPH_\mcA of _\mcPL2(\mcM,τ)_\mcA, generated by v vectors. The (modified) free entropy dimension of any generating set of \mcM 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.