Subgroup correspondences

Abstract

For a closed subgroup of a locally compact group the Rieffel induction process gives rise to a $C^{\ast }$-correspondence over the $C^{\ast }$-algebra of the subgroup. We study the associated Cuntz-Pimsner algebra and show that, by varying the subgroup to be open, compact, or discrete, there are connections with the Exel-Pardo correspondence arising from a cocycle, and also with graph algebras.

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