On unitary groups of crossed product von Neumann algebras

2022/12/22 by Yasuhito Hashiba, Hashiba, Yasuhito
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2212.11467

openalex publication_date 2022/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the tracial crossed product algebra M=A\rtimesΛ arising from a trace preserving action σ:Λ\curvearrowright A of a discrete group Λ on a tracial von Neumann algebra A. For a unitary subgroup G⊂ U(M), we study when this G can be conjugated into U(A)⋅Λ in M. We provide a general sufficient condition for this to happen. Our result generalizes a result of Ioana, Popa and Vaes, which treats the case when M is the group von Neumann algebra L(Λ).

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