Hilbert Modules over C*-categories

Abstract: C*-categories are a ‘horizontal categorification’ of C*-algebras, and they have a theory of Hilbert modules which generalizes that over C*-algebras. We go through some results about these modules, culminating in an Eilenberg-Watts theorem that characterizes which functors between module categories are given by tensor products. We finish with some new work employing this result, along with work of Benjamin Duenzinger’s, to exhibit a localization of the category of locally small C*-categories at the Morita equivalences.

geometric topologynumber theoryoperator algebrasrepresentation theory

Audience: researchers in the topic

( 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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