Induced representations and hypergroupoids (Q401233)

Holkar has introduced a notion of correspondences for groupoids that allows a proper generalization of Rieffel's results on Morita equivalence for transformation groups. Rieffel's work relies on his seminal contribution on strong Morita equivalence for \(C^*\)-algebras, where the notion of \(C^*\)-correspondence for two \(C^*\)-algebras \(A\) and \(B\) is introduced under the name Hermitian \(B\)-rigged \(A\)-module.NEWLINENEWLINEIn this paper, the author reviews different notions of correspondences for locally compact groupoids with Haar systems, including the one by R. D. Holkar, constructs representations induced by such correspondences, and extends these results to the case of hypergroupoids.