A. Marrakchi

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20242026

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5 papers · 1 filter

math.OA2026

Kadison's problem and ergodicity of the bicentralizer flow and

Amine Marrakchi

We solve Kadison's problem on the existence of maximal abelian subalgebras in irreducible subfactors $N \subset M$ when $N$ is AFD or when $N$ is with expectation in $M$ . In the la…

math.OA2026

Uniqueness of almost periodic outer flows on the hyperfinite type $II_{1}$ factor

Cyril Houdayer, Amine Marrakchi

We show that any almost periodic outer flow $I^\pm : R ↷ R$ on the hyperfinite type $II_{1}$ factor with Connes' spectrum $I^ (I^\pm) = R$ satisfies t…

math.OA2026

Selfless W $^{*}$ -probability spaces and Connes' bicentralizer problem

Cyril Houdayer, Amine Marrakchi

We introduce the notion of selfless W $^{*}$ -probability space and study its connection with Connes' bicentralizer problem. In particular, we show that if $M$ is a separable type ${\r…

math.OA2025

Almost almost periodic type $III_{1}$ factors and their 3-cohomology obstructions

Amine Marrakchi

We construct an exemple of a full factor $M$ such that its canonical outer modular flow $I ¨ ^{M} : R \to Out (M)$ is almost periodic but $M$ has no almost per…

math.OA2024

Kadison's problem for type III subfactors and the bicentralizer conjecture

Amine Marrakchi

In 1967, Kadison asked "if $N$ is a subfactor of the factor $M$ for which $N^{'} \cap M$ consists of scalars, will some maximal abelian *-subalgebra of $N$ be a maximal abelian subalg…

Kadison's problem and ergodicity of the bicentralizer flow and

Uniqueness of almost periodic outer flows on the hyperfinite type II1​ factor

Selfless W∗-probability spaces and Connes' bicentralizer problem

Almost almost periodic type III1​ factors and their 3-cohomology obstructions

Kadison's problem for type III subfactors and the bicentralizer conjecture

Uniqueness of almost periodic outer flows on the hyperfinite type $II_{1}$ factor

Selfless W $^{*}$ -probability spaces and Connes' bicentralizer problem

Almost almost periodic type $III_{1}$ factors and their 3-cohomology obstructions