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

Abstract: 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.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | video )

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Noncommutative geometry in NYC

Series comments: Noncommutative Geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. Our seminar welcomes talks in Number Theory, Geometric Topology and Representation Theory linked to the context of Operator Algebras. All talks are kept at the entry-level accessible to the graduate students and non-experts in the field. To join us click meet.google.com/zjd-ehrs-wtx (5 min in advance) and igor DOT v DOT nikolaev AT gmail DOT com to subscribe/unsubscribe for the mailing list, to propose a talk or to suggest a speaker. Pending speaker's consent, we record and publish all talks at the hyperlink "video" on speaker's profile at the "Past talks" section. The slides can be posted by providing the organizers with a link in the format "myschool.edu/~myfolder/myslides.pdf". The duration of talks is 1 hour plus or minus 10 minutes.

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