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arXiv · 2203.08690

Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras

Chris Bruce·Takuya Takeishi
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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 isomorphism class completely characterises the number field.

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Chris Bruce, Takuya Takeishi. 2022-03-16. Constructing number field isomorphisms from *-isomorphisms of certain crossed product C*-algebras. https://doi.org/10.1007/s00220-023-04927-y

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