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 crossed product. © 2011 London Mathematical Society.
CITATION STYLE
Carlsen, T. M., Larsen, N. S., Sims, A., & Vittadello, S. T. (2011). Co-universal algebras associated to product systems, and gauge-invariant uniqueness theorems. Proceedings of the London Mathematical Society, 103(4), 563–600. https://doi.org/10.1112/plms/pdq028
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