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Higher 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 ofExpand
Graphs, Groupoids, and Cuntz–Krieger Algebras
We associate to each locally finite directed graphGtwo locally compact groupoidsGandG(★). The unit space ofGis the space of one–sided infinite paths inG, andG(★) is the reduction ofGto the space ofExpand
We associate to each row-nite directed graph E a universal Cuntz-Krieger C-algebra C(E), and study how the distribution of loops in E aects the structure of C(E) .W e prove that C(E) is AF if andExpand
On C*-Diagonals
Approximately Central Matrix Units and the Structure of Noncommutative Tori
The property of approximate divisibility for C*-algebras is introduced and studied. Simple approximately divisible C*-algebras are shown to have nice nonstable K-theory properties. Non- rationalExpand
$C^*$-algebras of directed graphs and group actions
Given a free action of a group $G$ on a directed graph $E$ we show that the crossed product of $C^* (E)$, the universal $C^*$-algebra of $E$, by the induced action is strongly Morita equivalent toExpand
Fell bundles over groupoids
We study the C*-algebras associated to Fell bundles over groupoids and give a notion of equivalence for Fell bundles which guarantees that the associated C*-algebras are strong Morita equivalent. AsExpand
The Brauer group of a locally compact groupoid
<abstract abstract-type="TeX"><p>We define the Brauer group Br (<i>G</i>) of a locally compact groupoid <i>G</i> to be the set of Morita equivalence classes of pairs (<i>A</i>, α) consisting of anExpand
KMS states on C^*-algebras associated to expansive maps
Using Walters' version of the Ruelle-Perron-Frobenius Theorem we show the existence and uniqueness of KMS states for a certain one-parameter group of automorphisms on a C*-algebra associated to aExpand