Tight decomposition of factors and the single generation problem

2019/10/31 by Sorin Popa, Popa, Sorin · 1 citation
Mathematics · #46L10 #46L55 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1910.14653

openalex publication_date 2019/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A II₁ factor M has the \it stable single generation (\it SSG) property if any amplification M^t, t>0, can be generated as a von Neumann algebra by a single element. We discuss a conjecture stating that if M is SSG, then M has a \it tight decomposition, i.e., there exists a pair of hyperfinite II₁ subfactors R₀, R₁ ⊂ M such that R₀ \vee R₁^op=\Cal B(L²M). We explain why this conjecture is interesting and discuss possible approaches to prove it. We also prove some related results.

Cited by

• Compressible subalgebras in II₁ factors

Related

• Singly Generated II₁ Factors
• Coarse decomposition of II₁ factors
• McDuff superrigidity for group II₁ factors
• Non-embeddable II₁ factors resembling the hyperfinite II₁ factor
• Simplices of maximally amenable extensions in II₁ factors