Graph-Based Models for Kirchberg Algebras

By Jack Spielberg. 2005

60 citations recorded by the source corpus.

We give a construction of Kirchberg algebras from graphs. By using product graphs in the construction we are able to provide models for general (UCT) Kirchberg algebras while maintaining the explicit generators and relations of the underlying graphs.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/93d37f1f15a24a98ec80d0281e02b4cbd6dec8b3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Remarks on some fundamental results about higher-rank graphs and their C*-algebras (2011, methodology): “Indeed, Spielberg [25] showed how to construct every Kirchberg algebra from combinations of graph C∗-algebras and 2-graph C∗-algebras.”
Cartan subalgebras in C*-algebras. Existence and uniqueness (2017, methodology): “This is a slight modification of the construction in [58].”
Groupoids and C * -algebras for categories of paths (2011, methodology): “We give a generalization of the examples termed hybrid graph algebras that were constructed in [32], Definition 2.”
A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness (2008, unknown): “Spielberg constructed all non-unital Kirchberg algebras mixing the constructions of graph algebras and the higher rank graph algebras [ Sp1 ].”
Every classifiable simple C*-algebra has a Cartan subalgebra (2018, methodology): “). The dimension can be reduced to two if K1 is torsion-free (see Corollary 1.8 and Remark 3.9). In particular, together with the classiﬁcation results in [26, 36, 22, 14, 46], the groupoid models in [43], and [3, Theorem 3.1], we obtain the following Corollary 1.5. A unital separable simple C*-alge”