Haagerup and Størmer's conjecture for pointwise inner automorphisms

2023/09/11 by Yusuke Isono, Isono, Yusuke
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2309.05279

openalex publication_date 2023/09/11 · openalex created_date 2023/09/13 · openalex updated_date 2026/07/28

Abstract

In 1988, Haagerup and Størmer conjectured that any pointwise inner automorphism of a type \rm III₁ factor is a composition of an inner and a modular automorphism. We study this conjecture and prove that any type \rm III₁ factor with trivial bicentralizer indeed satisfies this condition. In particular, this shows that Haagerup and Størmer's conjecture holds in full generality if Connes' bicentralizer problem has an affirmative answer. Our proof is based on Popa's intertwining theory and Marrakchi's recent work on relative bicentralizers.

Related

• Pointwise inner automorphisms of almost periodic factors
• Full factors, bicentralizer flow and approximately inner automorphisms
• A type III₁ factor with the smallest outer automorphism group
• Kadison's problem for type III subfactors and the bicentralizer conjecture
• Autocentralizer automorphisms of groups