Jonathan Taylor (Göttingen): Morphisms between étale groupoids coming from C*-algebras. Oberseminar C*- Algebren.
Tuesday, 04.04.2023 16:15 im Raum SRZ 216/217
The obvious choice of arrow between two groupoids is a homomorphism (or functor). This works well enough until one wants to induce morphisms of groupoid C*-algebras. The problem that arises is that homomorphisms of groupoids would be covariant on the source and range fibres of the groupoid, but contravariant on the unit space, so a *-homomorphism of the C*-algebras would have to face both directions.
Buneci and Stachura introduce a different morphism of groupoids by considering actions of groupoids on other groupoids. They show that such morphisms covariantly induce *-homomorphisms of the groupoid C*-algebras. Meyer and Zhu call these morphisms 'actors' and build a categorical framework around the category of groupoids with actors as morphisms.
In this talk, I will define actors for étale (twists over) étale groupoids and show that any *-homomorphism between Cartan pairs which entwines all of the Cartan structure must come from an actor between the underlying groupoids. In this way an equivalence of categories is realised.
Angelegt am Thursday, 12.01.2023 11:43 von Elke Enning
Geändert am Thursday, 30.03.2023 15:02 von Elke Enning
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