Commuting-Square Subfactors and Central Sequences

2008/08/19 by Richard Burstein, Burstein, Richard
Mathematics · #46L37 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.0808.2487

openalex publication_date 2008/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M₀ ⊂ M₁ be a finite-index infinite-depth hyperfinite II₁ subfactor and ω a free ultrafilter of the natural numbers. We show that if this subfactor is constructed from a commuting square then the central sequence inclusion M₀^ω ∩ M₁' ⊂ (M₀)_ω has infinite Pimnser-Popa index. We will also demonstrate this result for certain infinite-depth hyperfinite subfactors coming from groups.

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