Indecomposability of free group factors over nonprime subfactors and abelian subalgebras
Abstract
We use the free entropy defined by D. Voiculescu to prove that the free group factors can not be decomposed as closed linear spans of noncommutative monomials in elements of nonprime subfactors or abelian $*$subalgebras, if the degrees of monomials have an upper bound depending on the number of generators. The resulting estimates for the hyperfinite and abelian dimensions of free group factors settle in the affirmative a conjecture of L. Ge and S. Popa (for infinitely many generators).
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 2004
 arXiv:
 arXiv:math/0402108
 Bibcode:
 2004math......2108S
 Keywords:

 Mathematics  Operator Algebras;
 46Lxx (Primary) 47Lxx (Secondary)