Product systems over Ore monoids

Abstract

We interpret the Cuntz–Pimsner covariance condition as a nondegeneracy condition for representations of product systems. We show that Cuntz–Pimsner algebras over Ore monoids are constructed through inductive limits and section algebras of Fell bundles over groups. We construct a groupoid model for the Cuntz–Pimsner algebra coming from an action of an Ore monoid on a space by topological correspondences. We characterise when this groupoid is effective or locally contracting and describe its invariant subsets and invariant measures.