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}
}

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References

SHOWING 1-10 OF 38 REFERENCES

Purely infinite C*-algebras arising from crossed products

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

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 II, EXAMPLES

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

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

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

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

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

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