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

2015/01/22 by Rennie, Adam, Robertson, David, Sims, Aidan · 2 citations
#46L05 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1501.05476

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.

Cited by

• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective
• Some remarks on Reduced C^*-algebras of semigroup dynamical systems and product systems

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