A complete characterisation of algebraic number fields using Cartan pairs

Chris Bruce

*(Queen Mary University of London and University of Glasgow)*

10:00-11:00, November 2, 2021 Zoom 922 3207 0952 (Passcode: C*-algebra)

__Abstract:__

Given any two rings of algebraic integers, Li and L¨ąck proved that the associated ring C*-algebras are always isomorphic. I will present a result showing that in stark contrast with the result by Li and L¨ąck: given any two such rings, there is a Cartan-preserving isomorphism between the ring C*-algebras if and only if the rings are isomorphic. As a consequence of this result, the semigroup C*-algebra of the (full) ax+b-semigroup over a ring of algebraic integers together with its canonical Cartan subalgebra completely characterises the ring. This is joint work with Xin Li (University of Glasgow).

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