Crossed Products by Dual Coactions of Groups and Homogeneous Spaces

TL;DR

This paper presents a new, more practical method for inducing representations of crossed products of C*-algebras by dual coactions, extending to homogeneous spaces and establishing an imprimitivity theorem.

Contribution

It offers an alternative, more workable construction of the bimodule for dual coactions based on the symmetric imprimitivity theorem, applicable to homogeneous spaces.

Findings

Provides a new construction for dual coactions

Extends the imprimitivity theorem to homogeneous spaces

Simplifies the induction process for representations

Abstract

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.