منابع مشابه
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 necessary and sufficient for the associated C∗-algebra to have topological dimension zero. We prove that a purely infinite 2-graph algebra has real-rank zero if and only if it has topological dimension zero and sat...
متن کاملHigher Rank Graph Algebras
These are lecture notes of a course given by Alex Kumjian at the RMMC Summer School at the University of Wyoming, Laramie, June 1-5, 2015. Warning: little proofreading has been done.
متن کاملHigher Rank Graph C∗-algebras
Building on recent work of Robertson and Steger, we associate a C∗–algebra to a combinatorial object which may be thought of as a higher rank graph. This C∗–algebra is shown to be isomorphic to that of the associated path groupoid. Various results in this paper give sufficient conditions on the higher rank graph for the associated C∗–algebra to be: simple, purely infinite and AF. Results concer...
متن کاملStable Rank and Real Rank of Graph C ∗ - Algebras
For a row finite directed graph E, Kumjian, Pask, and Rae-burn proved that there exists a universal C *-algebra C * (E) generated by a Cuntz-Krieger E-family. In this paper we consider two density problems of invertible elements in graph C *-algebras C * (E), and it is proved that C * (E) has stable rank one, that is, the set of all invertible elements is dense in C * (E) (or in its unitization...
متن کاملRepresentations of higher rank graph algebras
Let F+θ be a k-graph on a single vertex. We show that every irreducible atomic ∗-representation is the minimal ∗-dilation of a group construction representation. It follows that every atomic representation decomposes as a direct sum or integral of such representations. We characterize periodicity of F+θ and identify a symmetry subgroup Hθ of Z. If this has rank s, then C(Fθ ) ∼= C(T) ⊗ A for so...
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ژورنال
عنوان ژورنال: Indiana University Mathematics Journal
سال: 2017
ISSN: 0022-2518
DOI: 10.1512/iumj.2017.66.6212