Proper actions, fixed-point algebras and naturality in nonabelian duality
| dc.creator | Kaliszewski, S. | |
| dc.creator | Quigg, John | |
| dc.creator | Raeburn, Iain | |
| dc.date | 2007-12-30 | |
| dc.date | 2008-04-14 | |
| dc.date.accessioned | 2026-07-07T09:31:55Z | |
| dc.date.available | 2026-07-07T09:31:55Z | |
| dc.description | Suppose a locally compact group G acts freely and properly on a locally compact Hausdorff space X, and let gamma be the induced action on C_0(X). We consider a category in which the objects are C*-dynamical systems (A, G, alpha) for which there is an equivariant homomorphism of (C_0(X), gamma) into the multiplier algebra M(A). Rieffel has shown that such systems are proper and saturated, and hence have a generalized fixed-point algebra A^alpha which is Morita equivalent to A times_{alpha,r} G. We show that the assignment (A, alpha) maps to A^alpha is functorial, and that Rieffel's Morita equivalence is natural in a suitable sense. We then use our results to prove a categorical version of Landstad duality which characterizes crossed products by coactions, and to prove that Mansfield imprimitivity for crossed products by homogeneous spaces is natural. | |
| dc.description | 19 pages; minor revision | |
| dc.identifier | https://arxiv.org/abs/0801.0161 | |
| dc.identifier | http://arxiv.org/abs/0801.0161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158629 | |
| dc.subject | Operator Algebras | |
| dc.subject | Category Theory | |
| dc.subject | 46L55, 46M15, 18A25 | |
| dc.title | Proper actions, fixed-point algebras and naturality in nonabelian duality | |
| dc.type | text |