On unitary groups of crossed product von Neumann algebras

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On unitary groups of crossed product von Neumann algebras

Hashiba, Yasuhito

Journal of functional analysis, 04/2024, Volume: 286, Issue: 8

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We consider the tracial crossed product algebra M=A⋊Λ arising from a trace preserving action σ:Λ↷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 14, Theorem 3.1 which treats the case when M is the group von Neumann algebra L(Λ).

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