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Higher Rank Graph C-Algebras

- A. Kumjian, D. Pask
- Mathematics
- 5 July 2000

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… Expand

Graphs, Groupoids, and Cuntz–Krieger Algebras

- A. Kumjian, D. Pask, I. Raeburn, J. Renault
- Mathematics
- 1 March 1997

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 of… Expand

CUNTZ-KRIEGER ALGEBRAS OF DIRECTED GRAPHS

- A. Kumjian, D. Pask, I. Raeburn
- Mathematics
- 1 May 1998

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 and… Expand

Approximately Central Matrix Units and the Structure of Noncommutative Tori

- B. Blackadar, A. Kumjian, M. Rørdam
- Mathematics
- 1 May 1992

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- rational… Expand

$C^*$-algebras of directed graphs and group actions

- A. Kumjian, D. Pask
- Mathematics
- 1 December 1999

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 to… Expand

Fell bundles over groupoids

- A. Kumjian
- Mathematics
- 21 July 1996

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. As… Expand

The Brauer group of a locally compact groupoid

- A. Kumjian, Alexander Paul S. Jean N. Dana P. Muhly, Alexander Paul S. Jean N. Dana P. Renault, A. Williams
- Mathematics
- 17 June 1997

<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 an… Expand

KMS states on C^*-algebras associated to expansive maps

- A. Kumjian, J. Renault
- Mathematics
- 1 May 2003

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 a… Expand

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