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

@article{Carlsen2009CouniversalAA, title={Co‐universal algebras associated to product systems, and gauge‐invariant uniqueness theorems}, author={Toke Meier Carlsen and Nadia S. Larsen and Aidan Sims and Sean T. Vittadello}, journal={Proceedings of the London Mathematical Society}, year={2009}, volume={103} }

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…

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