Chris Bruce
(Newcastle University)
March 7, 2025
16:00
(UTC)
Organized by Americas GNCG Seminar.

On the C*-algebra of Connes’ adele class space

The multiplicative group of an algebraic number field acts by multiplication on the adele ring of the field, and the quotient space for this action is Connes’ adele class space. I will give an overview of joint work with Takuya Takeishi in which we prove that the crossed product C*-algebra associated with the adele class space completely remembers the number field. Precisely, we prove that two such crossed product C*-algebras are *-isomorphic if and only if the underlying number fields are isomorphic. Primitive ideals and subquotients play a central role in our proof.

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