The range of K-invariants for C*-algebras of infinite graphs

By Szymanski, Wojciech. 2002

54 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/861e6c642014127645f06a6534392d6bc70d0891

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Rank-two graphs whose C∗-algebras are direct limits of circle algebras (2005, background): “) In particular, it is now easy to decide whether a given graph algebra is simple and purely infinite, and a theorem of Szymański [34] says that every Kirchberg algebra with torsion-free K1 is isomorphic to a corner in a graph algebra.”
The ideal structure of the $C\sp *$-algebras of infinite graphs (2001, background): “Indeed, Szyma´nski has shown in [ 25 ] that every stable, purely infinite, simple and classifiable C ∗-algebra with K1 torsion-free can be realised as a graph”
Product systems of graphs and the Toeplitz algebras of higher-rank graphs | NOVA. The University of Newcastle's Digital Repository (2003, background): “of models for simple purely infinite algebras (see, for example, [13, 3, 9, 19 ]).”
UCT-Kirchberg algebras have nuclear dimension one (2014, unknown): “S S Let E K be the inﬁnite row-ﬁnite graph For each n apply [23, Theorem 1.2] to obtain a row-ﬁnite strongly connected graph E n such that C ∗ ( E n ) is a UCT Kirchberg algebra with K ∗ ( C ∗ ( E n )) = ( G n, 0 , F ( G n, 1 )).”
A class of C*-algebras generalizing both graph algebras and homeomorphism C*-algebras IV, pure infiniteness (2008, unknown): “The following lemma is inspired by [ Sz2 , Lemma 1.1].”
Graph-Based Models for Kirchberg Algebras (2005, background): “We mention Szymański’s proof [18] that any Kirchberg algebra with free K1-group can be realized as the C∗-algebra of an irreducible row-finite graph, and the proof in [15] that Kirchberg algebras having finitely generated Ktheory and free K1-group are semiprojective (in the sense of Blackadar).”
The path space of a directed graph (2011, methodology): “Graph C∗-algebras include (up to Morita equivalence) all AF algebras [4] and all Kirchberg algebras with free abelian K1 [17], as well many nonsimple examples of purely infinite nuclear C ∗-algebras.”