2022
DOI: 10.48550/arxiv.2203.08690
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Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras

Abstract: We prove that the class of crossed product C*-algebras associated with the action of the multiplicative group of a number field on its ring of finite adeles is rigid in the following explicit sense: Given any *-isomorphism between two such C*-algebras, we construct an isomorphism between the underlying number fields. As an application, we prove an analogue of the Neukirch-Uchida theorem using topological full groups, which gives a new class of discrete groups associated with number fields whose abstract isomor… Show more

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