Pushouts of extensions of groupoids by bundles of abelian groups
Publication Name
New Zealand Journal of Mathematics
Abstract
We analyse extensions σ 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 σ 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 σ, and that this isomorphism descends to an isomorphism of reduced algebras. We give a number of examples and applications.
Open Access Status
This publication may be available as open access
Volume
52
First Page
561
Last Page
581
Funding Number
209277
Funding Sponsor
Office of Naval Research