Journal of Operator Theory

Volume 39, Issue 1, Winter 1998 pp. 151-176.

Crossed products by dual coactions of groups and homogeneous spaces

Authors: Siegfried Echterhoff (1), S. Kaliszewski (2), and Iain Raeburn (3)
Author institution: (1) Fachbereich Mathematik-Informatik, Universitaet-Gesamthochschule Paderborn, D--33095 Paderborn, Germany
(2) Department of Mathematics, University of Newcastle, NSW 2308, Australia
(3) Department of Mathematics, University of Newcastle, NSW 2308, Australia

Summary: Mansfield showed how to induce representations of crossed products of $C^*$-algebras by coactions from crossed products by quotient groups and proved an imprimitivity theorem characterising these induced representations. We give an alternative construction of his bimodule in the case of dual coactions, based on the symmetric imprimitivity theorem of the third author; this provides a more workable way of inducing representations of crossed products of $C^*$-algebras by dual coactions. The construction works for homogeneous spaces as well as quotient groups, and we prove an imprimitivity theorem for these induced representations.

Keywords: $C^*$-algebra, coaction, crossed product, imprimitivity, homogeneous space

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