Please use this identifier to cite or link to this item: https://hdl.handle.net/1959.11/31872
Title: Groupoid Fell bundles for product systems over quasi-lattice ordered groups
Contributor(s): Rennie, Adam (author); Robertson, David  (author)orcid ; Sims, Aidan (author)
Publication Date: 2017-11
Early Online Version: 2017-03-16
DOI: 10.1017/S0305004117000202
Handle Link: https://hdl.handle.net/1959.11/31872
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.

Publication Type: Journal Article
Grant Details: ARC/DP120100507
Source of Publication: Mathematical Proceedings of the Cambridge Philosophical Society, 163(3), p. 561-580
Publisher: Cambridge University Press
Place of Publication: United Kingdom
ISSN: 1469-8064
0305-0041
Fields of Research (FoR) 2020: 490408 Operator algebras and functional analysis
Socio-Economic Objective (SEO) 2020: 280118 Expanding knowledge in the mathematical sciences
Peer Reviewed: Yes
HERDC Category Description: C1 Refereed Article in a Scholarly Journal
Appears in Collections:Journal Article
School of Science and Technology

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