# Simplicity of twisted C*-algebras of Deaconu--Renault groupoids

@inproceedings{Armstrong2021SimplicityOT, title={Simplicity of twisted C*-algebras of Deaconu--Renault groupoids}, author={Becky Armstrong and Nathan Brownlowe and Aidan Sims}, year={2021} }

We consider Deaconu–Renault groupoids associated to actions of finite-rank free abelian monoids by local homeomorphisms of locally compact Hausdorff spaces. We study simplicity of the twisted C*-algebra of such a groupoid determined by a continuous circle-valued groupoid 2-cocycle. When the groupoid is not minimal, this C*-algebra is never simple, so we focus on minimal groupoids. We describe an action of the quotient of the groupoid by the interior of its isotropy on the spectrum of the…

## 2 Citations

A uniqueness theorem for twisted groupoid C*-algebras

- Mathematics
- 2021

We present a uniqueness theorem for the reduced C*-algebra of a twist E over a Hausdorff étale groupoid G. We show that the interior IE of the isotropy of E is a twist over the interior IG of the…

Conjugacy of local homeomorphisms via groupoids and C*-algebras

- Mathematics
- 2021

We investigate dynamical systems consisting of a locally compact Hausdorff space equipped with a partially defined local homeomorphism. Important examples of such systems include self-covering maps,…

## References

SHOWING 1-10 OF 38 REFERENCES

Simplicity of twisted C*-algebras of higher-rank graphs and crossed products by quasifree actions

- Mathematics
- 2014

We characterise simplicity of twisted C*-algebras of row-finite k-graphs with no sources. We show that each 2-cocycle on a cofinal k-graph determines a canonical second-cohomology class for the…

Reconstruction of groupoids and C*-rigidity of dynamical systems

- Mathematics
- 2017

We show how to construct a graded locally compact Hausdorff \'etale groupoid from a C*-algebra carrying a coaction of a discrete group, together with a suitable abelian subalgebra. We call this…

SIMPLICITY OF TWISTED C*-ALGEBRAS OF TOPOLOGICAL HIGHER-RANK GRAPHS

- MathematicsBulletin of the Australian Mathematical Society
- 2020

In a recent series of papers, Kumjian, Pask and Sims [2–5] have investigated the effect of ‘twisting’ C∗-algebras associated to higher-rank graphs using a categorical 2-cocycle on the graph. This…

The Primitive Ideals of some Étale Groupoid C∗-Algebras

- Mathematics
- 2015

We consider the Deaconu–Renault groupoid of an action of a finitely generated free abelian monoid by local homeomorphisms of a locally compact Hausdorff space. We catalogue the primitive ideals of…

Simplicity of algebras associated to étale groupoids

- Mathematics
- 2012

We prove that the full C∗-algebra of a second-countable, Hausdorff, étale, amenable groupoid is simple if and only if the groupoid is both topologically principal and minimal. We also show that if G…

Graphs, Groupoids, and Cuntz–Krieger Algebras

- Mathematics
- 1997

We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space of…

On the K-theory of twisted higher-rank-graph C*-algebras

- Mathematics
- 2012

We investigate the K-theory of twisted higher-rank-graph algebras by adapting parts of Elliott's computation of the K-theory of the rotation algebras. We show that each 2-cocycle on a higher-rank…

Groupoid Crossed Products

- Mathematics
- 2009

We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the…

On twisted higher-rank graph C*-algebras

- Mathematics
- 2011

We define the categorical cohomology of a k-graphand show that the first three terms in this cohomology are isomorphic to the corresponding terms in the cohomology defined in our previous paper. This…

Groupoids associated with endomorphisms

- Mathematics
- 1995

To a compact Hausdorff space which covers itself, we associate an r-discrete locally compact Hausdorff groupoid. Its C*-algebra carries an action of the circle allowing it to be regarded as a crossed…