TY - JOUR
AU - Ionescu, Marius
AU - Kumjian, Alex
AU - Renault, Jean N.
AU - Sims, Aidan
AU - Williams, Dana P.
PY - 2021/09/19
Y2 - 2023/12/10
TI - Pushouts of extensions of groupoids by bundles of abelian groups
JF - New Zealand Journal of Mathematics
JA - NZ J Math
VL - 52
IS -
SE - Vaughan Jones Memorial Special Issue
DO - 10.53733/136
UR - https://nzjmath.org/index.php/NZJMATH/article/view/136
SP - 561--581
AB - <p>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.</p>
ER -