# 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}
}
• Published 26 June 2009
• Mathematics
• Proceedings of the London Mathematical Society
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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## References

SHOWING 1-10 OF 59 REFERENCES

The universal C*-algebras of discrete product systems generalize the Toeplitz–Cuntz algebras and the Toeplitz algebras of discrete semigroups. We consider a semigroup P which is quasi-lattice ordered
• Mathematics
• 2003
Let X be a Hilbert bimodule over a C*-algebra A. We analyse the structure of the associated Cuntz-Pimsner algebra O X and related algebras using representation-theoretic methods. In particular, we
• Mathematics
• 1997
A collection of partial isometries whose range and initial pro- jections satisfy a specified set of conditions often gives rise to a partial rep- resentation of a group. The corresponding C -algebra
A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X s : s E P} of Hilbert bimodules, indexed
Given a Fell bundle $\B$, over a discrete group $\Gamma$, we construct its reduced cross sectional algebra $C^*_r(\B)$, in analogy with the reduced crossed products defined for C*-dynamical systems.
We study the ideal structure of C*-algebras arising from C*-correspondences. We prove that gauge-invariant ideals of our C*-algebras are parameterized by certain pairs of ideals of original
• Mathematics
Journal of the Australian Mathematical Society
• 2002
Abstract The graph product of a family of groups lies somewhere between their direct and free products, with the graph determining which pairs of groups commute. We show that the graph product of
The Toeplitz C -algebras associated to quasi-lattice ordered groups (G,P) studied by Nica in (12) were shown by Laca and Raeburn ((7)) to be crossed products of an abelian C -algebra BP by a
• Mathematics
• 1994
Let r+ be the positive cone in a totally ordered abelian group F. We construct crossed products by actions of r1" as endomorphisms of C- algebras, and give criteria which ensure a given