Some free entropy dimension inequalities for subfactors

2004/10/28 by Kenley Jung, Jung, Kenley
Mathematics · #46L35 #46L54 #52C17 #Advanced Operator Algebra Research #FOS: Mathematics #Mathematical Inequalities and Applications #Operator Algebras (math.OA) #Point processes and geometric inequalities #math.OA #msc:46L35 #msc:46L54 #msc:52C17

paper · pdf · doi:10.48550/arxiv.math/0410594

11 pages

arxiv created 2004/10/28 · openalex publication_date 2004/10/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose N ⊂ M is an inclusion of II₁-factors of finite index. If N can be generated by a finite set of elements, then there exist finite generating sets X for N and Y for M such that δ₀(X) ≥ δ₀(Y), where δ₀ denotes Voiculescu's microstates (modified) free entropy dimension. Moreover given ε>0 one has δ₀(F) ≥ δ₀(G) ≥ ([M:N]^-2 -ε) ⋅ (δ₀(F) -1) + 1 - ε for certain generating sets F for N and G for M.

Related

• An estimate of free entropy and applications
• A Inequality for Non-Microstates Free Entropy Dimension for Crossed Products by Finite Abelian Groups
• All generating sets of all property T von Neumann algebras have free entropy dimension ≤ 1
• Remarks on free entropy dimension
• Infinite multiplicity of abelian subalgebras in free group subfactors