Indecomposability of free group factors over nonprime subfactors and abelian subalgebras

Details Indecomposability of free group factors over nonprime subfactors and abelian subalgebras Indecomposability of free group factors over nonprime subfactors and abelian subalgebras

2004-02-07

arxiv.org/abs/math/0402108v1

Mathematics

Operator Algebras

Scientific paper

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).

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