• Corpus ID: 119625506

Unbounded quasitraces, stable finiteness and pure infiniteness

@article{Pask2017UnboundedQS,
  title={Unbounded quasitraces, stable finiteness and pure infiniteness},
  author={David Pask and Adam Sierakowski and Aidan Sims},
  journal={arXiv: Operator Algebras},
  year={2017}
}
We prove that if A is a \sigma-unital exact C*-algebra of real rank zero, then every state on K_0(A) is induced by a 2-quasitrace on A. This yields a generalisation of Rainone's work on pure infiniteness and stable finiteness of crossed products to the non-unital case. It also applies to k-graph algebras associated to row-finite k-graphs with no sources. We show that for any k-graph whose C*-algebra is unital and simple, either every twisted C*-algebra associated to that k-graph is stably… 

Figures from this paper

Dense subalgebras of purely infinite simple groupoid C*-algebras

Abstract A simple Steinberg algebra associated to an ample Hausdorff groupoid G is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space

Ideal structure and pure infiniteness of ample groupoid $C^{\ast }$ -algebras

In this paper, we study the ideal structure of reduced $C^{\ast }$ -algebras $C_{r}^{\ast }(G)$ associated to étale groupoids $G$ . In particular, we characterize when there is a one-to-one

The Groupoids of Adaptable Separated Graphs and Their Type Semigroups

Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup,

Self-similar k-Graph C*-Algebras

  • Hui LiDilian Yang
  • Mathematics, Computer Science
    International Mathematics Research Notices
  • 2019
The main results generalize the recent work of Exel and Pardo on self-similar graphs and characterize the simplicity of ${{\mathcal{O}}}_{G,\Lambda }$ in terms of the underlying action, and prove that, whenever the action is simple, there is a dichotomy.

A dichotomy for groupoid $\text{C}^{\ast }$ -algebras

We study the finite versus infinite nature of C $^{\ast }$ -algebras arising from étale groupoids. For an ample groupoid $G$ , we relate infiniteness of the reduced C $^{\ast }$ -algebra

Purely infinite simple Steinberg algebras have purely infinite simple C*-algebras

A simple Steinberg algebra associated to an ample Hausdorff groupoid is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are

References

SHOWING 1-10 OF 62 REFERENCES

Non-simple purely infinite C∗-algebras: the Hausdorff case

Infinite Non-simple C*-Algebras: Absorbing the Cuntz Algebra O∞

Abstract The first named author has given a classification of all separable, nuclear C*-algebras A that absorb the Cuntz algebra O ∞. (We say that A absorbs O ∞ if A is isomorphic to A⊗ O ∞.)

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

Finiteness and Paradoxical Decompostions in C*-Dynamical Systems

We discuss the interplay between K-theoretical dynamics and the structure theory for certain C*-algebras arising from crossed products. For noncommutative C*-systems we present notions of minimality

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

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

Remarks on some fundamental results about higher-rank graphs and their C*-algebras

Abstract Results of Fowler and Sims show that every k-graph is completely determined by its k-coloured skeleton and collection of commuting squares. Here we give an explicit description of the

THE C -ALGEBRAS OF ROW-FINITE GRAPHS

NSKI Abstract. We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C -algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many

Discrete Crossed product C*-algebras

Classification of C*-algebras has been an active area of research in mathematics for at least half a century. In this thesis, we consider classification results related to the class of crossed

Real rank and topological dimension of higher rank graph algebras

We study dimension theory for the $C^*$-algebras of row-finite $k$-graphs with no sources. We establish that strong aperiodicity - the higher-rank analogue of condition (K) - for a $k$-graph is
...