Rennie, Adam

Robertson, David

Sims, Aidan

2017-11

<p>Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the product system. Under the additional hypothesis that the left actions in the product system are implemented by injective homomorphisms, we show that the cross-sectional algebra of the restriction of the bundle to a natural boundary subgroupoid coincides with the Cuntz-Nica-Pimsner algebra of the product system. We apply these results to improve on existing sufficient conditions for nuclearity of the Nica-Toeplitz algebra and the Cuntz-Nica-Pimsner algebra, and for the Cuntz-Nica-Pimsner algebra to coincide with its co-universal quotient.</p>

Mathematical Proceedings of the Cambridge Philosophical Society, 163(3), p. 561-580

1469-8064

0305-0041

https://hdl.handle.net/1959.11/31872

Cambridge University Press

Groupoid Fell bundles for product systems over quasi-lattice ordered groups

Journal Article

Publication