06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Jonathan Taylor (University of Potsdam)
Groupoid homomorphisms do not, generally, lift (functorially) to *-homomorphisms of the associated C*-algebras. The crux of this lies in the fact groupoids span a class of objects ranging from groups to topological spaces, and the C*-algebra construction is covariantly functorial for groups and their homomorphisms, but contravariantly functorial for spaces and their continuous maps.
Actors form an alternative morphism between groupoids which induce *-homomorphisms between C*-algebras while encompassing both group homomorphisms and (opposite) continuous maps. A natural question following this is, under what conditions is a *-homomorphism between groupoid C*-algebras induced by an actor of the underlying groupoids? In this talk I will provide a partial answer, showing a reconstruction of groupoid actors between effective groupoids from *-homomorphisms preserving certain (Cartan) structure of the C*-algebras.