TY - JOUR
AU - Rennie, Adam
AU - Robertson, David
AU - Sims, Aidan
PY - 2017/02/23
Y2 - 2024/06/14
TI - Groupoid algebras as Cuntz-Pimsner algebras
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 120
IS - 1
SE - Articles
DO - 10.7146/math.scand.a-25507
UR - https://www.mscand.dk/article/view/25507
SP - 115-123
AB - <p>We show that if $G$ is a second countable locally compact Hausdorff étale groupoid carrying a suitable cocycle $c\colon G\to\mathbb{Z}$, then the reduced $C^*$-algebra of $G$ can be realised naturally as the Cuntz-Pimsner algebra of a correspondence over the reduced $C^*$-algebra of the kernel $G_0$ of $c$. If the full and reduced $C^*$-algebras of $G_0$ coincide, we deduce that the full and reduced $C^*$-algebras of $G$ coincide. We obtain a six-term exact sequence describing the $K$-theory of $C^*_r(G)$ in terms of that of $C^*_r(G_0)$.</p>
ER -