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arXiv · 1501.05476

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

Adam Rennie·David Robertson·Aidan Sims
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Abstract

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.

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Adam Rennie, David Robertson, Aidan Sims. 2015-01-28. Groupoid Fell bundles for product systems over quasi-lattice ordered groups. https://arxiv.org/abs/1501.05476

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