Product Systems over Ore Monoids

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.

2010 Mathematics Subject Classification: 46L55, 22A22

Keywords and Phrases: Crossed product; product system; Ore conditions; Cuntz--Pimsner algebra; correspondence; groupoid model; higher-rank graph algebra; topological graph algebra.

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