Journal article

Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems

Toke M Carlsen, Nadia S Larsen, Aidan Sims, Sean T Vittadello

Proceedings of the London Mathematical Society | WILEY | Published : 2011

Abstract

Let (G, P) be a quasi-lattice ordered group, and let X be a product system over P of Hilbert bimodules. Under mild hypotheses, we associate to X a C*-algebra which is co-universal for injective Nica covariant Toeplitz representations of X which preserve the gauge coaction. Under appropriate amenability criteria, this co-universal C*-algebra coincides with the Cuntz-Nica-Pimsner algebra introduced by Sims and Yeend. We prove two key uniqueness theorems, and indicate how to use our theorems to realize a number of reduced crossed products as instances of our co-universal algebras. In each case, it is an easy corollary that the Cuntz-Nica-Pimsner algebra is isomorphic to the corresponding full c..

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Funding Acknowledgements

This research was supported by the Australian Research Council, The Research Council of Norway and The Danish Natural Science Research Council. Part of this work was completed while the first three authors were visiting the Fields Institute.We thank Narutaka Ozawa and Iain Raeburn for helpful conversations about coactions. We thank Marcelo Laca for helpful discussions about quasi-lattice ordered groups and boundary quotient algebras. The first three authors acknowledge both the financial support and the stimulating atmosphere of the Fields Institute.