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

2015/09/29 by Niels Meesschaert, Meesschaert, Niels
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Operator Algebras (math.OA) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1509.08645

openalex publication_date 2015/09/29 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

Let BS(n₁,m₁) curvearrowright X₁ and BS(n₂,m₂) curvearrowright X₂\nbe two ergodic essentially free probability measure preserving actions of\nnonamenable Baumslag-Solitar groups whose canonical almost normal abelian\nsubgroups act aperiodically. We prove that an isomorphism between the\ncorresponding crossed product II₁ factors forces BS(n₁,m₁) \≅\nBS(n₂,m₂) when |n₁| \≠ |m₁| and BS(n₁,m₁) \≅ BS(n₂,\±m₂)\nwhen |n₁| = |m₁|. This improves an orbit equivalence rigidity result obtained\nby Houdayer and Raum.\n

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