Functoriality for groupoid C*-algebras

03.07.2024, 10:15  –  Haus 9, Raum 2.22
Forschungsseminar: Gruppen und Operatoralgebren

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.