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- Title
PUSHOUTS OF EXTENSIONS OF GROUPOIDS BY BUNDLES OF ABELIAN GROUPS.
- Authors
IONESCU, MARIUS; KUMJIAN, ALEX; RENAULT, JEAN N.; SIMS, AIDAN; WILLIAMS, DANA P.
- 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.
- Subjects
GROUP extensions (Mathematics); GROUPOIDS; ALGEBRA; ABELIAN groups
- Publication
New Zealand Journal of Mathematics, 2021, Vol 52, p561
- ISSN
1171-6096
- Publication type
Article
- DOI
10.53733/136