Product systems over Ore monoids

Understand

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.