2022/01/24 by Dimitri Shlyakhtenko, Shlyakhtenko, D.
Computer Science · Mathematics · #46L37 #46L54 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical Dynamics and Fractals #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2201.09503
openalex publication_date 2022/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For certain generating sets of the subfactor pair M⊂ M\rtimes G where G is a finite abelian group we prove an approximate inequality between their non-microstates free entropy dimension, resembling the Shreier formula for ranks of finite index subgroups of free groups. As an application, we give bounds on free entropy dimension of generating sets of crossed products of the form M\rtimes(ℤ/2ℤ)⊕∞ for a large class of algebras M.