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 isomorphism class completely characterises the number field.

44 pages

References in corpus (3)

• K-theory for semigroup C*-algebras and partial crossed products
• C*-algebras from actions of congruence monoids on rings of algebraic integers
• On K-theoretic invariants of semigroup C*-algebras from actions of congruence monoids