Classification of Purely Infinite Graph C*-Algebras

Abstract: I will explain how purely infinite graph $C^*$-algebras may be classified up to stable isomorphism using an invariant of K-theoretic nature. This is contained in my recent preprint with Rasmus Bentmann. The key idea is to classify $C^*$-correspondences from a graph $C^*$-algebra to another $C^*$-algebra up to homotopy, using some projections and unitaries in the target $C^*$-algebra. Since we classify correspondences up to homotopy, we also classify general graph $C^*$-algebras up to homotopy equivalence. The relevant homotopies will automatically preserve gauge-invariant ideals, and we may improve this to also preserve the ideals that are not gauge invariant, if these are present.

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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