A TRINARY RELATION ARISING FROM A MATCHED PAIR OF R-DISCRETE GROUPOIDS

Abstract

We introduce a notion of a matched pair of r-discrete groupoids and that of a trinary relation associated with a matched pair. We construct three C^∗-algebras from a trinary relation and study properties of these algebras. The above results are applied to an action of a countable discrete semidirect product group on a topological space with an invariant measure.