Cuntz–Pimsner algebras of twisted partial automorphisms

Abstract: We will discuss how to construct a $C^*$-algebra from a vector bundle and a partial action of the integers on the base space of the bundle, using the machinery of Cuntz–Pimsner algebras. Despite being much more general, the resulting algebras share many properties with partial crossed products by the integers. They also generalise the $C^*$-algebras constructed from homeomorphisms twisted by vector bundles recently introduced by Adamo–Archey–Forough–Georgescu–Jeong–Strung–Viola. Under natural conditions on the action and the space, classifiability of the $C^*$-algebras is shown. In particular, we obtain both stably finite as well as purely infinite classifiable $C^*$-algebras from the same dynamical framework.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( paper | slides | 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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