The nuclear dimension of graph C*-algebras

@article{Ruiz2013TheND,
  title={The nuclear dimension of graph C*-algebras},
  author={Efren Ruiz and Aidan Sims and Mark Tomforde},
  journal={Advances in Mathematics},
  year={2013},
  volume={272},
  pages={96-123}
}
View PDF on arXiv
12 Citations
Background Citations
4
Methods Citations
3

12 Citations

Nuclear dimension of extensions of $\mathcal{O}_\infty$-stable algebras.

We obtain an improved upper bound for the nuclear dimension of extensions of $\mathcal{O}_\infty$-stable $\rm{C}^*$-algebras. In particular, we prove that the nuclear dimension of a full extension of…

UCT-Kirchberg algebras have nuclear dimension one

On the nuclear dimension of certain UCT-Kirchberg algebras

ALGEBRAS HAVE NUCLEAR DIMENSION ONE

. We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows.

The Cuntz–Toeplitz algebras have nuclear dimension one

Sturmian subshifts and their C*-algebras

This paper investigates the structure of C∗-algebras built from one-sided Sturmian subshifts. They are parametrised by irrationals in the unit interval and built from a local homeomorphism associated…

The Rokhlin property vs. Rokhlin dimension 1 on unital Kirchberg algebras

We investigate symmetries on unital Kirchberg algebras with respect to the Rokhlin property and finite Rokhlin dimension. In stark contrast to the restrictiveness of the Rokhlin property, every such…

KMS States on Generalised Bunce–Deddens Algebras and their Toeplitz Extensions

We study the generalised Bunce–Deddens algebras and their Toeplitz extensions constructed by Kribs and Solel from a directed graph and a sequence $$\omega $$ω of positive integers. We describe both…

Structure and classification of generalised bunce-deddens algebras and their KMS States

vi

The nuclear dimension of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:msub><mml:mrow><mml:mi mathvariant="script">O</mml:mi></mml:mrow><mml:mrow><mml:mo>∞</mml:mo></mml:mrow></mml:msub></mml:math>-stable C⁎-algebras

References

SHOWING 1-10 OF 37 REFERENCES

Graph C*-Algebras with Real Rank Zero

Given a row-finite directed graph E, a universal C*-algebra C*(E) generated by a family of partial isometries and projections subject to the relations determined by E is associated to the graph E.…

The nuclear dimension of C*-algebras

Stability of C^*-algebras associated to graphs

We characterize stability of graph C*-algebras by giving five conditions equivalent to their stability. We also show that if G is a graph with no sources, then C*(G) is stable if and only if each…

Ideals in Graph Algebras

We show that the graph construction used to prove that a gauge-invariant ideal of a graph C ∗ -algebra is isomorphic to a graph C ∗ -algebra, and also used to prove that a graded ideal of a Leavitt…

Nuclear dimension and -stability of pure C ∗ -algebras

In this article I study a number of topological and algebraic dimension type properties of simple C*-algebras and their interplay. In particular, a simple C*-algebra is defined to be (tracially)…

Purely Infinite Cuntz–Krieger Algebras of Directed Graphs

For arbitrary infinite directed graphs E, the characterisation of the (not necessarily simple) Cuntz–Krieger algebras C*(E) which are purely infinite in the sense of Kirchberg–Rørdam is given. It is…

A Class of Limit Algebras Associated with Directed Graphs

Abstract Every directed graph defines a Hilbert space and a family of weighted shifts that act on the space. We identify a natural notion of periodicity for such shifts and study their C* -algebras.…

The Toeplitz algebra of a Hilbert bimodule

Suppose a C*-algebra A acts by adjointable operators on a Hilbert A-module X. Pimsner constructed a C*-algebra O_X which includes, for particular choices of X, crossed products of A by Z, the Cuntz…

Decomposition rank of UHF-absorbing c* -algebras

Let A be a unital separable simple C*-algebra with a unique tracial state. We prove that if A is nuclear and quasidiagonal, then A tensored with the universal UHF-algebra has decomposition rank at…

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…