# Purely infinite simple C*-algebras that are principal groupoid C*-algebras

@article{Brown2015PurelyIS, title={Purely infinite simple C*-algebras that are principal groupoid C*-algebras}, author={Jonathan Henry Brown and Lisa Orloff Clark and Adam Sierakowski and Aidan Sims}, journal={arXiv: Operator Algebras}, year={2015} }

## 6 Citations

### All classifiable Kirchberg algebras are C∗-algebras of ample groupoids

- MathematicsExpositiones Mathematicae
- 2020

### A Tool Kit for Groupoid 𝐶*-Algebras

- MathematicsMathematical Surveys and Monographs
- 2019

∗ -algebras. Selfadjoint ∗ -algebras, von ( W ∗ algebras, etc.) -modules. – their algebras – C ∗ -algebras and W ∗ -algebras

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

- Mathematics
- 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…

### Cartan subalgebras in C*-algebras. Existence and uniqueness

- MathematicsTransactions of the American Mathematical Society
- 2019

We initiate the study of Cartan subalgebras in C*-algebras, with a particular focus on existence and uniqueness questions. For homogeneous C*-algebras, these questions can be analyzed systematically…

### Ample groupoids: equivalence, homology, and Matui's HK conjecture

- Mathematics
- 2018

We investigate the homology of ample Hausdorff groupoids. We establish that a number of notions of equivalence of groupoids appearing in the literature coincide for ample Hausdorff groupoids, and…

### Purely infinite labeled graph $C^{\ast }$ -algebras

- MathematicsErgodic Theory and Dynamical Systems
- 2019

In this paper, we consider pure infiniteness of generalized Cuntz–Krieger algebras associated to labeled spaces $(E,{\mathcal{L}},{\mathcal{E}})$ . It is shown that a $C^{\ast }$ -algebra $C^{\ast…

## References

SHOWING 1-10 OF 38 REFERENCES

### Purely infinite C*-algebras arising from crossed products

- MathematicsErgodic Theory and Dynamical Systems
- 2011

Abstract We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of…

### C*-algebras by example

- Mathematics
- 1996

The basics of C*-algebras Normal operators and abelian C*-algebras Approximately finite dimensional (AF) C*-algebras $K$-theory for AF C*-algebras C*-algebras of isometries Irrational rotation…

### A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness

- Mathematics
- 2005

### A CLASS OF C*-ALGEBRAS GENERALIZING BOTH GRAPH ALGEBRAS AND HOMEOMORPHISM C*-ALGEBRAS II, EXAMPLES

- Mathematics
- 2004

We show that the method to construct C*-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from…

### GRAPH INVERSE SEMIGROUPS, GROUPOIDS AND THEIR C -ALGEBRAS

- Mathematics
- 2002

We develop a theory of graph C -algebras using path groupoids and inverse semigroups. Row finiteness is not assumed so that the theory applies to graphs for which there are vertices emitting a…

### Viewing AF-algebras as graph algebras

- Mathematics
- 1998

Every AF-algebra A arises as the C*-algebra of a locally finite pointed directed graph in the sense of Kumjian, Pask, Raeburn, and Renault. For AF-algebras, the diagonal subalgebra defined by…

### 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…

### Groupoids and C * -algebras for categories of paths

- Mathematics
- 2011

In this paper we describe a new method of defining C*-algebras from oriented combinatorial data, thereby generalizing the constructions of algebras from directed graphs, higher-rank graphs, and…

### Morita Equivalence and Continuous-Trace $C^*$-Algebras

- Mathematics
- 1998

The algebra of compact operators Hilbert $C^*$-modules Morita equivalence Sheaves, cohomology, and bundles Continuous-trace $C^*$-algebras Applications Epilogue: The Brauer group and group actions…