Kadison's problem and ergodicity of the bicentralizer flow and

Amine Marrakchi

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arXiv · 2606.23636

Kadison's problem and ergodicity of the bicentralizer flow and

Amine Marrakchi

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Abstract

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 latter case, we first show that the relative bicentralizer flow of a type $\mathrm{III}_1$ irreducible subfactor with expectation is always ergodic. This also implies that for every irreducible subfactor with expectation $N \subset M$, there exists an AFD subfactor with expectation $P \subset N$ that is irreducible in $M$.

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Amine Marrakchi. 2026-06-22. Kadison's problem and ergodicity of the bicentralizer flow and. https://arxiv.org/abs/2606.23636

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