Naturality of Symmetric Imprimitivity Theorems

2011/03/21 by Astrid an Huef, Huef, Astrid an, S. Kaliszewski +5
Mathematics · #46L55 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:46L55

paper · pdf · doi:10.48550/arxiv.1103.4111

10 Pages, Revised abstract and introduction. No other changes

arxiv created 2011/05/30 · arxiv updated 2011/05/31

Abstract

The first imprimitivity theorems identified the representations of groups or dynamical systems which are induced from representations of a subgroup. Symmetric imprimitivity theorems identify pairs of crossed products by different groups which are Morita equivalent, and hence have the same representation theory. Here we consider commuting actions of groups H and K on a C^*-algebra which are saturated and proper as defined by Rieffel in 1990. Our main result says that the resulting Morita equivalence of crossed products is natural in the sense that it is compatible with homomorphisms and induction processes.

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