2004/02/07 by Marius Stefan, Marius Ştefan, Stefan, Marius
Mathematics · #46Lxx (Primary) 47Lxx (Secondary) #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46Lxx #msc:47Lxx
paper · pdf · doi:10.48550/arxiv.math/0402108
arxiv created 2004/02/07 · openalex publication_date 2004/02/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).