Infinite multiplicity of abelian subalgebras in free group subfactors

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/0402107

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

Abstract

We obtain an estimate of Voiculescu's (modified) free entropy dimension for generators of a II₁-factor \mcM with a subfactor \mcN containing an abelian subalgebra \mcA of finite multiplicity. It implies in particular that the interpolated free group subfactors of finite Jones index do not have abelian subalgebras of finite multiplicity or Cartan subalgebras.

Citations

• Applications of Free Entropy to Finite von Neumann Algebras, II

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