Dauns-Hofmann-Kumjian-Renault Duality for Fell Bundles and Structured C*-Algebras

Tristan Bice (Czech Academy of Sciences in Prague)

Thursday 15th June, 2023 16:00-17:00 Maths 311B


A natural problem that has plagued C*-algebra theory since its inception has been to find an appropriate noncommutative extension of the classic Gelfand duality, thus truly justifying the viewpoint of C*-algebra theory being "noncommutative topology".  Here we outline our work to unify two of the more successful such extensions, namely the C*-bundle construction of Dauns and Hofmann from the late 60's and the more recent Weyl groupoid construction of Kumjian and Renault.  We do this via ultrafilters, inspired by a somewhat forgotten paper of Milgram from the late 40's, allowing for a more direct construction of the required groupoid.  Our construction is also functorial with respect to a general class of morphisms between Fell bundles akin to those considered by Varela between C*-bundles back in the 70's.

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