The Brauer Group of a Locally Compact Groupoid
| dc.creator | Kumjian, Alex | |
| dc.creator | Muhly, Paul S. | |
| dc.creator | Renault, Jean N. | |
| dc.creator | Williams, Dana P. | |
| dc.date | 1997-06-17 | |
| dc.date.accessioned | 2026-07-07T09:13:48Z | |
| dc.date.available | 2026-07-07T09:13:48Z | |
| dc.description | We define the Brauer group $\Br(G)$ of a locally compact groupoid $G$ to be the set of Morita equivalence classes of pairs $(\A,α)$ consisting of an elementary C*-bundle $\A$ over $G^{(0)}$ satisfying Fell's condition and an action $α$ of $G$ on $\A$ by $*$-isomorphisms. When $G$ is the transformation groupoid $X\times H$, then $\Br(G)$ is the equivariant Brauer group $\Br_H(X)$. In addition to proving that $\Br(G)$ is a group, we prove three isomorphism results. First we show that if $G$ and $H$ are equivalent groupoids, then $\Br(G)$ and $\Br(H)$ are isomorphic. This generalizes the result that if $G$ and $H$ are groups acting freely and properly on a space $X$, say $G$ on the left and $H$ on the right then $\Br_G(X/H)$ and $\Br_H(G/ X)$ are isomorphic. Secondly we show that the subgroup $\Br_0(G)$ of $\Br(G)$ consisting of classes $[\A,α]$ with $\A$ having trivial Dixmier-Douady invariant is isomorphic to a quotient $\E(G)$ of the collection $\Tw(G)$ of twists over $G$. Finally we prove that $\Br(G)$ is isomorphic to the inductive limit $\Ext(G,T)$ of the groups $\E(G^X)$ where $X$ varies over all principal $G$ spaces $X$ and $G^X$ is the imprimitivity groupoid associated to $X$. | |
| dc.description | 52 pages AMS-LaTeX | |
| dc.identifier | https://arxiv.org/abs/funct-an/9706004 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9706004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152453 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | The Brauer Group of a Locally Compact Groupoid | |
| dc.type | text |