Proper actions, fixed-point algebras and naturality in nonabelian duality

dc.creatorKaliszewski, S.
dc.creatorQuigg, John
dc.creatorRaeburn, Iain
dc.date2007-12-30
dc.date2008-04-14
dc.date.accessioned2026-07-07T09:31:55Z
dc.date.available2026-07-07T09:31:55Z
dc.descriptionSuppose 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.description19 pages; minor revision
dc.identifierhttps://arxiv.org/abs/0801.0161
dc.identifierhttp://arxiv.org/abs/0801.0161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/158629
dc.subjectOperator Algebras
dc.subjectCategory Theory
dc.subject46L55, 46M15, 18A25
dc.titleProper actions, fixed-point algebras and naturality in nonabelian duality
dc.typetext

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