Groupoid Fell bundles for product systems over quasi-lattice ordered groups

@article{Rennie2015GroupoidFB,
  title={Groupoid Fell bundles for product systems over quasi-lattice ordered groups},
  author={Adam Graham Rennie and David I. Robertson and Aidan Sims},
  journal={Mathematical Proceedings of the Cambridge Philosophical Society},
  year={2015},
  volume={163},
  pages={561 - 580}
}
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… 
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References

SHOWING 1-10 OF 29 REFERENCES

C*-algebras associated to product systems of hilbert bimodules

Let (G,P) be a quasi-lattice ordered group and let X be a compactly aligned product system over P of Hilbert bimodules. Under mild hypotheses we associate to X a C*-algebra which we call the…

Amenability for Fell bundles over groupoids

We establish conditions under which the universal and reduced norms coincide for a Fell bundle over a groupoid. Specifically, we prove that the full and reduced C � -algebras of any Fell bundle over…

Boundary quotients and ideals of Toeplitz C∗-algebras of Artin groups

Topological aperiodicity for product systems over semigroups of Ore type

Semigroup Crossed Products and the Toeplitz Algebras of Nonabelian Groups

Abstract We consider the quasi-lattice ordered groups ( G ,  P ) recently introduced by Nica. We realise their universal Toeplitz algebra as a crossed product B P ⋊ P by a semigroup of endomorphisms,…

PARTIAL DYNAMICAL SYSTEMS AND C -ALGEBRAS GENERATED BY PARTIAL ISOMETRIES

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…

Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers

Abstract We study the Toeplitz algebra 𝒯(ℕ⋊ℕ×) and three quotients of this algebra: the C*-algebra 𝒬ℕ recently introduced by Cuntz, and two new ones, which we call the additive and multiplicative…

Semicrossed Products of Operator Algebras by Semigroups

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive…

Inverse semigroups and combinatorial C*-algebras

Abstract.We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term tight. These representations are supported on a subset of the spectrum of the…

On Nuclearity of $C^{*}$ -algebras of Fell Bundles over Etale Groupoids

In this paper, we show that if E is a Fell bundle over an amenable \'etale locally compact Hausdorff groupoid such that every fiber on the unit space is nuclear, then $C?^*r(E)$ is also nuclear. In…