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arXiv · 1509.08645

A rigidity result for crossed products of actions of Baumslag-Solitar groups

Niels Meesschaert
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Abstract

Let BS(n_1,m_1) $\curvearrowright$ X_1 and BS(n_2,m_2) $\curvearrowright$ X_2 be two ergodic essentially free probability measure preserving actions of nonamenable Baumslag-Solitar groups whose canonical almost normal abelian subgroups act aperiodically. We prove that an isomorphism between the corresponding crossed product II_1 factors forces BS(n_1,m_1) $\cong$ BS(n_2,m_2) when |n_1| $\neq$ |m_1| and BS(n_1,m_1) $\cong$ BS(n_2,$\pm$m_2) when |n_1| = |m_1|. This improves an orbit equivalence rigidity result obtained by Houdayer and Raum.

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Niels Meesschaert. 2015-11-01. A rigidity result for crossed products of actions of Baumslag-Solitar groups. https://arxiv.org/abs/1509.08645

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