Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 057, 18 pages      arXiv:1402.0072      https://doi.org/10.3842/SIGMA.2014.057
Contribution to the Special Issue on Noncommutative Geometry and Quantum Groups in honor of Marc A. Rieffel

Induced Representations and Hypergroupoids

Jean Renault
Université d'Orléans et CNRS (UMR 7349 et FR2964), Département de Mathématiques, F-45067 Orléans Cedex 2, France

Received February 01, 2014, in final form May 26, 2014; Published online June 03, 2014

Abstract
We review various notions of correspondences for locally compact groupoids with Haar systems, in particular a recent definition due to R.D. Holkar. We give the construction of the representations induced by such a correspondence. Finally, we extend the construction of induced representations to hypergroupoids.

Key words: groupoids; $C^*$-algebras; correspondences; induced representations; hypergroups.

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