Cuntz-Nica-Pimsner algebras associated to product systems over quasi-lattice ordered groupoids

Abstract

We characterize Cuntz-Nica-Pimsner algebras for compactly aligned product systems over quasi-lattice ordered groupoids. We show that the full cross sectional $C^{\ast }$-algebras of Fell bundles of Morita equivalence bimodules are isomorphic to the related Cuntz-Nica-Pimsner algebras under certain conditions.