Subgroup correspondences

TL;DR

This paper explores the relationships between Rieffel induction, Cuntz-Pimsner algebras, and various classes of subgroups in locally compact groups, revealing connections with Exel-Pardo correspondences and graph algebras.

Contribution

It introduces new links between subgroup types and operator algebra constructions, expanding understanding of their interrelations.

Findings

Connections with Exel-Pardo correspondences from cocycles

Relations between subgroup types and graph algebras

Insights into the structure of Cuntz-Pimsner algebras

Abstract

For a closed subgroup of a locally compact group the Rieffel induction process gives rise to a $C^*$-correspondence over the $C^*$-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.