Regularity of induced representations and a theorem of Quigg and Spielberg

Abstract

Mackey's imprimitivity theorem characterizes the unitary representations of a locally compact group G which have been induced from representations of a closed subgroup K; Rieffel's influential reformulation says that the group C*-algebra C*(K) is Morita equivalent to the crossed product C0(G/K)×G [14]. There have since been many important generalizations of this theorem, especially by Rieffel [15, 16] and by Green [3, 4]. These are all special cases of the symmetric imprimitivity theorem of [11], which gives a Morita equivalence between two crossed products of induced C*-algebras.