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Article Dans Une Revue Année : 2021

Pushouts of extensions of groupoids by bundles of abelian groups

Résumé

We analyse extensions $\Sigma$ of groupoids G by bundles A of abelian groups. We describe a pushout construction for such extensions, and use it to describe the extension group of a given groupoid G by a given bundle A. There is a natural action of Sigma on the dual of A, yielding a corresponding transformation groupoid. The pushout of this transformation groupoid by the natural map from the fibre product of A with its dual to the Cartesian product of the dual with the circle is a twist over the transformation groupoid resulting from the action of G on the dual of A. We prove that the full C*-algebra of this twist is isomorphic to the full C*-algebra of $\Sigma$, and that this isomorphism descends to an isomorphism of reduced algebras. We give a number of examples and applications.

Dates et versions

hal-03903905 , version 1 (16-12-2022)

Identifiants

Citer

Marius Ionescu, Alex Kumjian, Jean Renault, Aidan Sims, Dana Williams. Pushouts of extensions of groupoids by bundles of abelian groups. 2021, 52, pp.561-581. ⟨10.53733/136⟩. ⟨hal-03903905⟩
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