Naturality of Rieffel's Morita equivalence for proper actions
| dc.creator | Huef, Astrid an | |
| dc.creator | Kaliszewski, S. | |
| dc.creator | Raeburn, Iain | |
| dc.creator | Williams, Dana P. | |
| dc.date | 2008-10-15 | |
| dc.date.accessioned | 2026-07-07T10:10:35Z | |
| dc.date.available | 2026-07-07T10:10:35Z | |
| dc.description | Suppose that a locally compact group $G$ acts freely and properly on the right of a locally compact space $T$. Rieffel proved that if $α$ is an action of $G$ on a $C^*$-algebra $A$ and there is an equivariant embedding of $C_0(T)$ in $M(A)$, then the action $α$ of $G$ on $A$ is proper, and the crossed product $A\rtimes_{α,r}G$ is Morita equivalent to a generalised fixed-point algebra $\Fix(A,α)$ in $M(A)^α$. We show that the assignment $(A,α)\mapsto\Fix(A,α)$ extends to a functor $\Fix$ on a category of $C^*$-dynamical systems in which the isomorphisms are Morita equivalences, and that Rieffel's Morita equivalence implements a natural isomorphism between a crossed-product functor and $\Fix$. From this, we deduce naturality of Mansfield imprimitivity for crossed products by coactions, improving results of Echterhoff-Kaliszewski-Quigg-Raeburn and Kaliszewski-Quigg Raeburn, and naturality of a Morita equivalence for graph algebras due to Kumjian and Pask. | |
| dc.identifier | https://arxiv.org/abs/0810.2819 | |
| dc.identifier | http://arxiv.org/abs/0810.2819 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171638 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55 | |
| dc.title | Naturality of Rieffel's Morita equivalence for proper actions | |
| dc.type | text |