Abstract

We use the free entropy defined by D. Voiculescu to prove that the free group factors cannot 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 afirmative a conjecture of L. Ge and S. Popa (for infinitely many generators).

Keywords

free entropy, free group factors

Mathematical Subject Classification

Primary: 46L54

Secondary: 46L35

Authors